Ionly have to do eleven of these but i’m stuck and it’s sin , cos , tan

5. 77.32°

6. 54.46°

7. 13.6

8. 19.5

9. 6.5

10. 12.6

Step-by-step explanation:

I find the mnemonic SOH CAH TOA to be extremely helpful for problems like this. It reminds you ...

Sin = Opposite/Hypotenuse

Cos = Adjacent/Hypotenuse

Tan = Opposite/Adjacent

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Based on your notes of problems 5 ad 6, I'd say you need to be a little careful of notation. The relationship between angles and side ratios is ...

• TrigFunction(angle) = ratio . . . . . . . . trig functions are sin, cos, tan, csc, sec, cot

• InverseTrigFunction(ratio) = angle . . . inverse trig functions are arcsin, arccos, arctan, arccsc, arcsec, arccot. These are also written with a -1 superscript, for example, sin⁻¹ for arcsin.

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5. sin(x°) = 40/41 . . . . . . . . . . . . opposite/hypotenuse

x° = arcsin(40/41) ≈ 77.32°

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6. tan(x°) = 7/5 . . . . . . . . . . . . . . opposite/adjacent

x° = arctan(7/5) ≈ 54.46°

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7. tan(39°) = 11/x

x = 11/tan(39°) . . . . . . . . . multiply both sides of the equation by x/tan(39°)

x ≈ 13.6

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8. cos(46°) = x/28

x = 28·cos(46°) ≈ 19.5

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9. tan(51°) = 8/x

x = 8/tan(51°) ≈ 6.5 . . . . . solve as in problem 7

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10. sin(24°) = x/31

x = 31·sin(24°) ≈ 12.6