Circular Functions V Lower Sixth Science Mathematics

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Test your trig identities and equation skills.

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Circular Functions V Lower Sixth Science Mathematics


Froggy Jumps Circular Functions V Lower Sixth Science MathematicsOnline version Test your trig identities and equation skills. by YAKILI LMS 1 What is the graph of arcsin x called? a Inverse sine graph b Sine wave graph c Cosine graph 2 Which property holds for sin^2 x + cos^2 x? a Equals 0 b Equals 2 c Equals 1 3 If sin x = 1/2, which is a possible x (principal value)? a x = 30° b x = 90° c x = 60° 4 Which identity is a Pythagorean one? a 1 + tan^2 x = sec^2 x b sin^2 x = cos^2 x c 1 - tan^2 x = cos^2 x 5 Which is a double-angle formula? a tan 2x = sin x cos x b sin 2x = 2sin x cos x c cos 2x = 2cos^2 x − 1 6 Which is a compound-angle identity? a sin(a + b) = sin a cos b + cos a sin b b sin(a − b) = sin a − sin b c cos(a + b) = cos a cos b − sin a sin b 7 Which equation solves trig functions? a Ignore domain issues b Only use graphs c Use inverse trig functions 8 What is the graph of tan x on its principal period? a Flat lines b Straight lines with vertical asymptotes c Wavy curves 9 Which identity relates sin and cos without tan? a sin x + cos x = 1 b sin^2 x + cos^2 x = 1 c tan^2 x + 1 = sec^2 x 10 Which is a valid double-angle formula for sin? a sin 2x = sin^2 x + cos^2 x b sin 2x = 2 sin x cos x c cos 2x = 2 cos^2 x - 1 11 What is the identity for cos 2x in terms of cos x only? a cos 2x = 1 − 2sin^2 x b cos 2x = sin^2 x − cos^2 x c cos 2x = 2cos^2 x − 1 12 Which is true about inverse trig functions domain? a Only complex values b Unrestricted domain c Restricted to principal value 13 What is tan^2 x + 1 equal to? a csc^2 x b sec^2 x c cos^2 x 14 Which formula expands cos(a + b)? a cos a sin b + sin a cos b b sin a sin b − cos a cos b c cos a cos b − sin a sin b 15 If sin x = 0, what is cos x? a ±1 b ±0.5 c 0 16 Which identity is used to simplify sin^2 x + cos^2 x? a Double-angle identity b Compound-angle identity c Pythagorean identity 17 Which is a valid form of cos 2x? a tan x b sin 2x c cos^2 x − sin^2 x 18 What does arcsin return? a An angle b A ratio c A length 19 Which identity is used to derive tan x in terms of sin and cos? a tan x = sin^2 x + cos^2 x b tan x = sin x / cos x c tan x = cos x / sin x 20 Which is true about inverse cosine graph? a Defined on [−1,1] b Defined outside [−1,1] c All real numbers 21 Which is a double-angle formula for cos? a cos 2x = 2sin x cos x b cos 2x = cos^2 x − sin^2 x c cos 2x = 1 − tan^2 x 22 Which equation solves for x in sin x = 0.5? a x = 0° + 360°k b x = 30° + 360°k or 150° + 360°k c x = 45° + 90°k 23 Which is a property of arcsin's range? a Range is [-π/2, π/2] b [0, 2π] c [-π, π] 24 Which identity relates sin 3x? a sin 3x = 3cos x − 4cos^3 x b sin 3x = 3sin x − 4sin^3 x c sin 3x = sin^3 x 25 What is the compound-angle formula for cos(a − b)? a cos a cos b − sin a sin b b sin a cos b − cos a sin b c cos a cos b + sin a sin b 26 Which identity is used to simplify tan half-angle? a Weierstrass substitution b Double-angle identity c Pythagorean identity 27 What does arctan return? a A length b A ratio c An angle 28 Which identity expresses sin^2 x in terms of cos 2x? a sin^2 x = cos 2x b sin^2 x = (1 − cos 2x)/2 c sin^2 x = (1 + cos 2x)/2 29 If cos x = 0, what is tan x? a 1 b 0 c Not defined 30 Which identity gives cos(a + b) in expanded form? a sin a sin b − cos a cos b b cos a sin b + sin a cos b c cos a cos b − sin a sin b 31 Which is a form of tan 2x? a tan 2x = 2tan x / (1 − tan^2 x) b tan 2x = sin x / cos x c tan 2x = tan x 32 What is the principal value of arccos 0? a 0 b π c π/2 33 Which identity can derive sec^2 x from cos x? a sec^2 x = cos^2 x b sec^2 x = 1 − cos^2 x c sec^2 x = 1 / cos^2 x 34 Which is a valid form of sin 2x in a product-to-sum context? a sin 2x = tan x b sin 2x = sin^2 x + cos^2 x c sin 2x = 2sin x cos x 35 For inverse trig, the range of arctan is? a (-π, π) b [0, π] c (-π/2, π/2) 36 Which identity is used for cos 2x in terms of sin x? a cos 2x = 1 − 2sin^2 x b cos 2x = 2sin^2 x − 1 c cos 2x = sin x cos x 37 What does sin−1(−1) equal? a 0 b π/2 c −π/2 38 Which is true for the period of sin graph? a 2π b π c π/2 39 Which trigonometric graph forms a wave? a Sine and cosine graphs b Cosecant only c Tangent only 40 Which identity is not a standard Pythagorean one? a tan^2 x + 1 = sin^2 x b 1 + tan^2 x = sec^2 x c sin^2 x + cos^2 x = 1 41 Which is an example of a compound-angle identity? a tan(a + b) = tan a + tan b b sin(a + b) = sin a cos b + cos a sin b c cos(a + b) = cos a cos b − sin a sin b 42 What is the principal value of arctan(1)? a π/4 b 0 c π/2 43 What is the range of arcsin x? a [-pi, pi] b [0, pi] c [-pi/2, pi/2] 44 Solve sin x = 1/2 in [0, 2pi). a x = pi/3 b x = pi/6 or 5pi/6 c x = pi/2 45 Which identity is Pythagorean? a sin^2 x - cos^2 x = 1 b tan^2 x + 1 = sec^2 x c sin^2 x + cos^2 x = 1 46 Cosine of sum identity is? a cos(a+b) = cos a cos b − sin a sin b b cos(a+b) = sin a sin b − cos a cos b c cos(a+b) = sin a cos b + cos a sin b 47 Double-angle formula for sine is? a sin 2x = 2 sin x cos x b sin 2x = sin x cos x c sin 2x = 2 cos^2 x 48 arctan range is? a [0, pi] b (-pi, pi) c (-pi/2, pi/2) 49 If cos 2x = 0, which are x in [0, 2pi)? a x = pi/4, 3pi/4, 5pi/4, 7pi/4 b x = 0 or pi c x = pi/6 or pi/3 50 Identity: sin^2 x equals? a 1 − cos^2 x b 2 sin x cos x c cos^2 x − 1

Circular Functions V Lower Sixth Science Mathematics

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Circular Functions V Lower Sixth Science MathematicsOnline version

by YAKILI LMS

What is the graph of arcsin x called?

Which property holds for sin^2 x + cos^2 x?

If sin x = 1/2, which is a possible x (principal value)?

Which identity is a Pythagorean one?

Which is a double-angle formula?

Which is a compound-angle identity?

Which equation solves trig functions?

What is the graph of tan x on its principal period?

Which identity relates sin and cos without tan?

Which is a valid double-angle formula for sin?

What is the identity for cos 2x in terms of cos x only?

Which is true about inverse trig functions domain?

What is tan^2 x + 1 equal to?

Which formula expands cos(a + b)?

If sin x = 0, what is cos x?

Which identity is used to simplify sin^2 x + cos^2 x?

Which is a valid form of cos 2x?

What does arcsin return?

Which identity is used to derive tan x in terms of sin and cos?

Which is true about inverse cosine graph?

Which is a double-angle formula for cos?

Which equation solves for x in sin x = 0.5?

Which is a property of arcsin's range?

Which identity relates sin 3x?

What is the compound-angle formula for cos(a − b)?

Which identity is used to simplify tan half-angle?

What does arctan return?

Which identity expresses sin^2 x in terms of cos 2x?

If cos x = 0, what is tan x?

Which identity gives cos(a + b) in expanded form?

Which is a form of tan 2x?

What is the principal value of arccos 0?

Which identity can derive sec^2 x from cos x?

Which is a valid form of sin 2x in a product-to-sum context?

For inverse trig, the range of arctan is?

Which identity is used for cos 2x in terms of sin x?

What does sin−1(−1) equal?

Which is true for the period of sin graph?

Which trigonometric graph forms a wave?

Which identity is not a standard Pythagorean one?

Which is an example of a compound-angle identity?

What is the principal value of arctan(1)?

What is the range of arcsin x?

Solve sin x = 1/2 in [0, 2pi).

Which identity is Pythagorean?

Cosine of sum identity is?

Double-angle formula for sine is?

arctan range is?

If cos 2x = 0, which are x in [0, 2pi)?

Identity: sin^2 x equals?