PRE CALCULUS Trigonometry 3

Question 1

Using the sum formula, what is the exact value of sin(75°)?

Accepted Answer

(√6 + √2)/4

Answer

sin(75°) = sin(45° + 30°) = sin45·cos30 + cos45·sin30 = (√2/2)(√3/2) + (√2/2)(1/2) = (√6 + √2)/4.

Question 2

The Law of Cosines, c² = a² + b² - 2ab·cos(C), reduces to the Pythagorean theorem when:

Accepted Answer

C = 90°

Answer

When C = 90°, cos(90°) = 0, so the -2ab·cos(C) term vanishes and c² = a² + b².

Question 3

What is the reference angle for 210°?

Accepted Answer

30°

Answer

210° is in the third quadrant; its reference angle is 210° - 180° = 30°.

Question 4

Which equation represents the inverse relationship arcsin(x)?

Accepted Answer

y = arcsin(x) means sin(y) = x for -π/2 ≤ y ≤ π/2

Answer

arcsin(x) = y means sin(y) = x, and the range is restricted to [-π/2, π/2] to make it a function.

Question 5

In a triangle, if A = 30°, a = 5, and b = 8, the Law of Sines gives sin(B) equal to:

Accepted Answer

4/5

Answer

sin(B)/b = sin(A)/a → sin(B) = b·sin(A)/a = 8·(1/2)/5 = 4/5.

PRE CALCULUS Practice Test