Y1, C10 - Trigonometric Identities & Equations

Question 1

What do supplementary angles sum to

Answer 1

180

Question 2

What do complementary angles sum to

Answer 2

90

Question 3

What is the cofunction indentity

Answer 3

sinx = cos(90 - x)
cosx = sin(90 - x)

Question 4

What is sin(90 - x) equal to

Answer 4

cosx

Question 5

What does the hypotenuse of a triangle describe

Answer 5

The gradient of the hypotenuse (tan x)

Question 6

What is the opposite side of angle x equal to

Answer 6

Hsin x
h = hypotenuse

Question 7

What is adjacent side of angle x equal to

Answer 7

Hcos x
h = hypotenuse

Question 8

What is positive in the 2nd quadrant of a CAST diagram and why

Answer 8

cosx = -ve (x value is negative)
sinx = +ve (y value is positive)
tanx = -ve (gradient is negative)

Question 9

What is sin(180 - x) equal to

Answer 9

sin(x)

Question 10

What is cos(360 - x) equal to

Answer 10

cos(x)

Question 11

Given that sinx is obtuse, would cosx and tanx be +ve or -ve

Answer 11

Both -ve

Question 12

Given that cosx = -3/5 is reflex, would sinx and tanx be +ve or -ve

Answer 12

sinx must be -ve as reflex angle lands in both T and C quadrants
tanx is sinx / cosx and -ve / -ve = +ve

Question 13

What are sinx and cosx equal to

Answer 13

sinx = (180 - x)
cosx = (360 -x)

Question 14

What does arc mean

Answer 14

Inverse
e.g. arcsin = sin^-1