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 18. A DVD rotates through an angle of 20 π radians in 1 second. At this speed, how many revolutions does the DVD make in 1 minute? Prove each trigonometric identity. 1.sinθsecθ = tanθ 2. cot (– θ) = – cotθ 3. cos 2 θ(sec 2 θ – 1) = sin 2 θ Rewrite each expression in terms of cosθ, and simplify. 4. cscθtanθ 5. (1 + sec 2 θ)(1 – sin 2 θ) 6. sin 2 θ + cos 2 θ + tan 2 θ 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 ° ° Draw an angle with the given measure in standard position. Then determine the measure of its reference angle