Lesson 6 Hidden Identities Practice Understanding

Ready

Use the diagram to help you find the two angles, , that are solutions to the equation. Round your answers to decimals. (Your calculator should be set in radians.)

Circle divided into four sectors with 0, 1.57, 3.14, and 4.17 radians 1.57 radians0 radians4.71 radians3.14 radians

Example: Show these steps for each problem.

Step 1: Write the value the calculator gives you when you ask it for the angle. .

0.7297

Step 2: Sketch that angle onto the diagram.

Circle divided into five sectors with 0, 1.57, 3.14, and 4.17 radians and sector with theta = 0.73 1.57 radians0 radians4.71 radians3.14 radians

Step 3: Ask yourself where else on the diagram will sine be positive and have the same reference angle.

Circle divided into six sectors with 0, 1.57, 3.14, and 4.17 radians and sectors with theta = 0.73 1.57 radians0 radians4.71 radians3.14 radians

Add that reference angle and the angle of rotation to the diagram. Calculate the angle of rotation for the second angle.

Step 4. Write the two solutions to the equation.

1.

calculator value:

two angles:

Circle divided into four sectors with 0, 1.57, 3.14, and 4.17 radians 1.57 radians0 radians4.71 radians3.14 radians

2.

calculator value:

two angles:

Circle divided into four sectors with 0, 1.57, 3.14, and 4.17 radians 1.57 radians0 radians4.71 radians3.14 radians

3.

calculator value:

two angles:

Circle divided into four sectors with 0, 1.57, 3.14, and 4.17 radians 1.57 radians0 radians4.71 radians3.14 radians

4.

calculator value:

two angles:

Circle divided into four sectors with 0, 1.57, 3.14, and 4.17 radians 1.57 radians0 radians4.71 radians3.14 radians

Set

5.

Use the values in the table to verify the Pythagorean identity ().

Then write the value of tangent .

6.

Label the angles of rotation and the coordinate points around the unit circle on the right. Then use these points to help you fill in the blank.

Blank unit circle with (1,0) (1, 0)

7.

Label the angles of rotation and the coordinate points around the unit circle on the right. Then use these points to help you fill in the blank.

Blank unit circle with (1,0)

8.

Use the graph of to help you fill in the blank.

Graph of sin(theta) x–2π–2π–2π–π–π–ππππy–2–2–2222000

Go

9.

Find the radian measure of the central angle of a circle of radius, , that intercepts an arc of length .

Round answers to decimal places.

Radius

Arc Length

Angle Measure in radians