Question

Find the sine, cosine, and tangent of 45 degrees.

Answer 1

30°, 45° and 60°

Explanation:

Sine, Cosine and Tangent

Because the radius is 1, we can directly measure sine, cosine and tangent.

unit circle center angle 0

What happens when the angle, θ, is 0°?

cos 0° = 1, sin 0° = 0 and tan 0° = 0

unit circle center angle 90

What happens when θ is 90°?

cos 90° = 0, sin 90° = 1 and tan 90° is undefined

Answer 2

√2/2, √2/2, 1

Explanation:

On a unit circle, sine is the y-coordinate, cosine is the x-coordinate, and tangent is the slope.

Tangent: since the angle is 45°, it is right between 90° and 0°. As the image shows, that place is where x = y. Therefore, the slope is 1.

Cosine + Sine: We can find the intersection of x = y and x² + y² = 1:

Substitute: x² + x² = 1

Simplify: 2x² = 1

Divide: x² = 1/2

x = y = ±√1/2 = ±1/√2 = ±√2/2

Since we are looking for the cos and sin of 45°, both numbers will be positive. So, √2/2.

(In the end it comes down to how well you know the unit circle, this will be easier with practice and familiarity)