Question

Express the given trigonometric functions in terms of the same function of a positive acute angle.sec 948 degrees, cos(-948) degrees

Answer 1

Given the Trigonometric Functions:

`\begin{gathered} sec(948\text{\degree}) \\ \\ cos(-948\text{\degree}) \end{gathered}`

Using your calculator you get:

`sec(948\text{\degree})\approx-1.49`

By definition, Secant is negative in Quadrant III.

Finds its Reference Angle as follows:

`948\text{\degree}-5\cdot180\text{\degree}=48\text{\degree}`

Because:

`(948)/(180)\approx5`

Then, you get:

`=-sec\left(48\text{\degree}\right)`

Notice that:

`cos(-948\text{\degree})\approx-0.67`

Then, you can conclude that it is in Quadrant II.

Therefore its Reference Angle is:

`5\cdot180\text{\degree}-948\text{\degree}=-48`

So you can set up:

`=-cos\lparen-48)`

By definition:

`cos(-\theta)=cos\theta`

Therefore, you can rewrite it in this form:

`=-cos(48\text{\degree})`

Hence, the answer is:

`\begin{gathered} sec(48\text{\degree}) \\ \\ -cos(48\text{\degree}) \end{gathered}`