Before you read

Answer first — see what you already know.

A navigator knows that $sin (40°) = a$ . Without a calculator, what is $cos (50°)$ ?

A
$\frac{1}{a}$
B
$1 - a$
C
$90 - a$
D
$a$

Check your answer

Answer:

Before you read

Answer first — see what you already know.

An architect designs a roof where $sin (3 x + 10) ° = cos (2 x - 5) °$ . Find $x$ .

A
25
B
15
C
19
D
17

Check your answer

Answer:

Theory

The Cofunction Identity

For any acute angle $x$ :
$\sin(x) = \cos(90° - x) \qquad \cos(x) = \sin(90° - x)$

This is because in a right triangle, the two acute angles are complementary ( $x + (90° - x) = 90°$ ), and the side opposite one angle is adjacent to the other.

sin(A) = cos(90°−A): complementary angle relationship

In radians: $\sin(\theta) = \cos(\frac{\pi}{2} - \theta)$

Example 1

If $\sin(25°) = 0.4226$ , what is $\cos(65°)$ ?

$65° = 90° - 25°$

So $\cos(65°) = \sin(25°) = 0.4226$

0.4226

Strategy

SAT Pro Tip

The SAT loves this identity! If you see $\sin(x°) = \cos(y°)$ , then $x + y = 90$ . This is tested almost every time and is a quick 30-second solve.

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