NBT NBT Mathematics: Trigonometry 1

Question 1

If sin θ = 3/5 and θ is in the first quadrant, what is cos θ?

Accepted Answer

4/5

Answer

Using the Pythagorean identity, cos θ = √(1 − sin²θ) = √(1 − 9/25) = √(16/25) = 4/5.

Question 2

What is the exact value of sin 30° × cos 60°?

Accepted Answer

1/4

Answer

sin 30° = 1/2 and cos 60° = 1/2, so their product is 1/4.

Question 3

In which quadrant is θ if sin θ < 0 and cos θ > 0?

Accepted Answer

Quadrant IV

Answer

In Quadrant IV, sine is negative and cosine is positive, matching the given conditions.

Question 4

Simplify: sin²x + cos²x + tan²x − sec²x

Accepted Answer

0

Answer

sin²x + cos²x = 1, and tan²x − sec²x = −1, so the full expression equals 1 + (−1) = 0.

Question 5

The period of y = sin(2x) is:

Accepted Answer

π

Answer

The period of y = sin(bx) is 2π/b; with b = 2, the period is 2π/2 = π.

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