Question

Can someone help me solve this

Answer 1

sin x = -5/13

csc x = -13/5

sec x = 13/12

cot x = -12/5

tan x = -5/12

Explanation:

**x is in quadrant iv because 3pi/2<x<2pi

• if cos x=12/13, then 12 is the adjacent value and 13 is the hypotenuse value. to find sin, or opposite/hypotenuse, use the pythagorean identity. opposite=5 and hypotenuse is given as 13. & since it's in quad iv, the sine (or y) value is negative bc it's below the x axis. thus, sin x = -5/13
• csc is cosecant, or the reciprocal of sine. so csc x = -13/5
• sec is secant, or the reciprocal of cosine. so sec x = 13/12
• tan is opp/adj, so tan x = -5/12. it's negative bc tan is negative in quad iv
• cot is cotangent, or the reciprocal of tangent. so cot x = -12/5

Answer 2

8. sin x = -5/13

9. csc x = -13/5

10. sec x = 13/12

11. cot x = -12/5

12. tan x = -5/12

Explanation:

The mnemonic SOH CAH TOA can help you with the sine and tangent. You need to rely on your memory (or notes) to find the reciprocal functions.

The dimensions are such that you can recognize this as a 5-12-13 right triangle. Or, you can use the Pythagorean theorem to find the third side from ... O = -√(H² -A²) = -√(169 -144) = -√25 = -5

The given quadrant tells you that O is negative.

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8. Sin = Opposite/Hypotenuse

Here, the opposite is -5. The hypotenuse is always taken to be positive.

sin x = -5/13

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9. Csc = 1/Sin

csc x = -13/5

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10. Sec = 1/Cos

sec x = 13/12

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11. Cot = 1/Tan = Adjacent/Opposite

cot x = 12/-5

cot x = -12/5

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12. Tan = Opposite/Adjacent

tan x = -5/12