2. Trigonometric Functions on Right Triangles

Find the exact value of the variables in each figure.

Use trigonometric function values of quadrantal angles to evaluate each expression. 3 sec 180° ― 5 tan 360°

Which right triangle contains an acute angle where the $\sin$ and $\cos$ of that angle are equal?

Concept Check Suppose that the point (x, y) is in the indicated quadrant. Determine whether the given ratio is positive or negative. Recall that r = √(x² + y²) .(Hint: Drawing a sketch may help.) I , y/r

Sketch an angle θ in standard position such that θ has the least positive measure, and the given point is on the terminal side of θ. Then find the values of the six trigonometric functions for each angle. Rationalize denominators when applicable. See Examples 1, 2, and 4. (―2√3 , 2)

Use the appropriate reciprocal identity to find each function value. Rationalize denominators when applicable. See Example 1.

sin θ , given that csc θ = √24/3

Find the exact value of the variables in each figure.

If $\(\sin\]\theta\)=\(\frac{\sqrt{17}\)}{17}$, find the values of the five other trigonometric functions. Rationalize the denominators if necessary.

Solve each problem. Height of a Lunar Peak The lunar mountain peak Huygens has a height of 21,000 ft. The shadow of Huygens on a photograph was 2.8 mm, while the nearby mountain Bradley had a shadow of 1.8 mm on the same photograph. Calculate the height of Bradley. (Data from Webb, T., Celestial Objects for Common Telescopes, Dover Publications.)

Determine the signs of the trigonometric functions of an angle in standard position with the given measure. See Example 2.

―345°

Find two angles in the interval [0°, 360°) that satisfy each of the following. Round answers to the nearest degree. tan θ = 1.3763819

If $m\angle ABC$ = $20°$ in a right triangle, what is the value of $\sin 20°$ rounded to two decimal places?

Concept Check Suppose that 90° < θ < 180° .   Find the sign of each function value. tan θ/2

If you know the radius of the circle and the measure of an angle $\theta$ in standard position, which trigonometric function gives the ratio of the length of the side opposite $\theta$ to the hypotenuse in a right triangle?

In Exercises 63–68, find the exact value of each expression. Do not use a calculator. tan(𝜋/3)/2 - 1/sec(𝜋/6)