Transcript 4-1: Tangents

4-6: Reciprocal Trig Functions
and Trigonometric Identities
Unit 4: Circles
English Casbarro
If the terminal side of angle θ lies on one of the axes, the angle θ is called a
quadrantal angle. The quadrantal angles are 0°, 90°, 180°, and 270°.
Complete the chart
to the right with the
correct
signs
This is one of the first trigonometric
identities given. There are others that you
can find as well.
You can use trigonometric identities to simplify trigonometric expressions.
Turn in the following problems
Prove each trigonometric identity.
1. sinθsecθ = tanθ
2. cot (– θ) = – cotθ
3. cos2θ(sec2θ – 1) = sin2θ
Rewrite each expression in terms of cosθ, and simplify.
4. cscθtanθ
5. (1 + sec2θ)(1 – sin2θ) 6. sin2θ + cos2θ + tan2θ
Use the unit circle to find the exact value of each trigonometric function.
7. sin150°
8. tan315°
9. cot
10. cos
Use a reference angle to find the exact value of the sine, cosine, and tangent of
each angle.
11. 240°
12. 120°
13.
14.
Draw an angle with the given measure in standard position. Then determine the
measure of its reference angle.
15.
16.
17.
18. A DVD rotates through an angle of 20π radians in 1 second.
At this speed, how many revolutions does the DVD make
in 1 minute?