# SAT MATH QUESTIONS ON TRIGONOMETRY

Question 1 : Given right triangle ABC above, which of the following is equal to c/b?

A) tanB

B) 1/tanB

C) cosB

D) 1/cosB

In all the given answer choices, we have the angle measure B. Considering the interior angle of B in the right triangle ABC above, AC is the opposite side and AB is adjacent side.

Length of the opposite side = AC = b

Length of the adjacent side = AB = c

The ratio between opposite side and adjacent side is "tan".

b/c = tanB

Take reciprocal on both sides.

c/b = 1/tanB

The correct answer choice is (B).

Question 2 :

sinx = cosy

In the equation above, x and y are measured in radians. Which of the following could be x in terms of y?

A) π/2 - y

B) π/2 + y

C) y - π/2

D) π - y

Since sinx and cosx are equal, the angles measures x and y are complementary.

x + y = 90° or π/2

x + y = π/2

x = π/2 - y

The correct answer choice is (A).

Question 3 :

What is the value of sin30° - cos60°?

A) 0

B) (1 - √3)/2

C) (√2 - 1)/2

D) (√3 - 1)/2

From the trigonometric ratio table, we have

sin30° = 1/2

cos60° = 1/2

sin30° - cos60° = 1/2 - 1/2

= 0

The correct answer choice is (A).

Question 4 : In the triangle above, AB = BC, what is the value of sinA?

A) 0.28

B) 0.56

C) 0.84

D) 0.96

In an isosceles triangle, perpendicular drawn to the unequal side will bisect it.

In the triangle ABC above, since AB = AC, it is an isosceles triangle. So, the perpendicular drawn to the unequal side AC will bisect it. In the right ΔABD, using Pythagorean Theorem,

72 + BD2 = 252

49 + BD2 = 625

BD2 = 576

BD2 = 242

BD = 24

In the right ΔABD,

sinA = opposite side/ hypotenuse

= BD/AB

= 24/25

= 0.96

The correct answer choice is (D).

Question 5 : Given right triangle ABC above, which of the following gives the length of AB in terms of θ?

A) sinθ

B) cosθ

C) tanθ

D) 1/sinθ

In the right ΔABC above, considering angle θ at the vertex B,

opposite side = AC

hypotenuse = BC

The length of the hypotenuse is given, that is BC = 1 and we have to find the length of the adjacent side.

The ratio between adjacent side and hypotenuse is "cos".

AB/BC = cosθ

AB/1 = cosθ

AB = cosθ

The correct answer choice is (B).

Question 6 : In the xy-plane above, a circle with radius 5 has its center at the origin. Point A lies on the circle and has coordinates (m, n). What is n in terms θ?

A) 5sinθ

B) 5cosθ

C) tanθ

D) 5(sinθ + cosθ)

In the given figure, draw a perpendicular from point A to x-axis. Let the perpendicular meet x-axis at B. Considering θ in the right ΔOAB in the figure above,

opposite side = AB = n

adjacent side = OB = m

hypotenuse = OA = 5

The length of the hypotenuse is given, that is OA = 5 and we have to find the length of the opposite side AB, that is n.

The ratio between opposite side and hypotenuse is "sin".

AB/OA = sinθ

n/5 = sinθ

n = 5sinθ

The correct answer choice is (A).

Question 7 : Right triangle ABC is shown in the xy-plane above. What is the value of tanA?

A) 7/12

B) 3/4

C) 7/9

D) 12/7

In the right ΔABC above, considering the angle A,

opposite side = BC

Length of the opposite side :

= BC

= y-coordinate at C - y-coordinate at B

= 4 - (-3)

= 7

Length of the adjacent side :

= AC

= x-coordinate at C - x-coordinate at B

= 7 - (-5)

= 7 + 5

= 12

= BC/AC

= 7/12

The correct answer choice is (A).

Question 8 :

sin24° = cos(3k + 6)°

In the equation above, the angle measures are in degrees. If 0° < k < 90°, what is the value of k?

Since sin24° and cos(3k + 6)° are equal, then the angles measures 24° and (3k + 6)° are complementary.

24° + (3k + 6)° = 90°

24 + 3k + 6 = 90

3k + 30 = 90

3k = 60

k = 20

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