Question

Suppose cosθ= -12/13 and sinθ > 0Determine the values of each of the other 5 trig functions.

Answer 1

step 1

Find the value of sin

we have that

`\sin ^2(\theta)+\cos ^2(\theta)=1^{}`

substitute the value of cosine

`\begin{gathered} \sin ^2(\theta)+(-(12)/(13))^2=1^{} \\ \\ \sin ^2(\theta)^{}=1^{}-((144)/(169)) \\ \\ \sin ^2(\theta)^{}=((25)/(169)) \\ \\ \sin ^{}(\theta)^{}=(5)/(13) \end{gathered}`

step 2

Find tan

`\tan (\theta)=(\sin (\theta))/(\cos (\theta))`

substitute the given values

`\tan (\theta)=-(5)/(12)`

step 3

Find cot

`\cot (\theta)=(1)/(\tan (\theta))`

substitute

`\cot (\theta)=-(12)/(5)`

step 4

Find sec

`\sec (\theta)=(1)/(\cos (\theta))`

substitute

`\sec (\theta)=-(13)/(12)`

step 5

Find csc

`\csc (\theta)=(1)/(\sin (\theta))`

substitute

`\csc (\theta)=(13)/(5)`