If tan(b)=-12/5 and angle b is in quadrant 4 Find the following Sin, Cos, Cot?

Question

2. Sec(θ)=-√13/2 and θ is in quadrant 3

3. Giiven θ is in quadrant 2 sin(θ)=8/17 what is the csc(θ), and cot(θ) and cos(θ)

4. The terminal side of angle a passes through point P(3,-4) Find Sin(A), Sec(A) and cot(A)

Answer 1

1)

Recall basic ratios of trigonometry.

From pythagorean theorem,

Angle b is in fourth quadrant .

Answer 2

2)

Recall basic ratios of trigonometry.

sec(θ) = [Hypotenuse]/[Adjacent side]

From pythagorean theorem,

Opposite side = √[(Hypotenuse)² - (Adjacent side)²]

Opposite side = 3

θ is in third quadrant .

sin(θ) = [Opposite side]/[Hypotenuse]

csc(θ) = [Hypotenuse]/[Opposite side]

cos(θ) = [Adjacent side]/[Hypotenuse]

cot(θ) = [Adjacent side]/[Opposite side]

tan(θ) = [Opposite side]/[Adjacent side]

Answer 3

3)sin(θ) = 8/17

Recall basic ratios of trigonometry.

sin(θ) = [Opposite side]/[Hypotenuse]

From pythagorean theorem,

Adjacent side = √[(Hypotenuse)² - (Opposite side)²]

= √[(17)² - (8)²]

= √(289 - 64)

= √225

Adjacent side = 15

θ is in second quadrant .

csc(θ) = [Hypotenuse]/[Opposite side]

csc(θ) = 17/8

cot(θ) = [Adjacent side]/[Opposite side]

cot(θ) = -(15/8)

cos(θ) = [Adjacent side]/[Hypotenuse]

cos(θ) = -(15/17).

Answer 4

4)P(3, -4)

The above coordinate pair in fourth quadrant.

Angle A is in fourth quadrant.

From pythagorean theorem,

r² = x² + y²

r = √(3² + 4²)

r = √(9 + 16)

r = √25

r = 5

sin(A) = y/r

sin(A) = -4/5

sec(A) = r/x

sec(A) = 5/3

cot(A) = x/y

cot(A) = -3/4.