How do we convert angle measures between degrees and radians?

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Presentation transcript:

How do we convert angle measures between degrees and radians? The Unit Circle Essential Questions How do we convert angle measures between degrees and radians? How do we find the values of trigonometric functions on the unit circle? Holt McDougal Algebra 2 Holt Algebra 2

You can use reference angles and Quadrant I of the unit circle to determine the values of trigonometric functions. Trigonometric Functions and Reference Angles

Students All The diagram shows how the signs of the trigonometric functions depend on the quadrant containing the terminal side of θ in standard position. Take Calculus

und.

Using Reference Angles to Evaluate Trigonometric Functions Use a reference angle to find the exact value of the sine, cosine, and tangent of each angle. Students All Take Calculus Step 1 Find the reference angle. Step 2 Find the sin, cos, and tan of the reference angle. Step 3 Adjust the signs, if needed.

Using Reference Angles to Evaluate Trigonometric Functions Use a reference angle to find the exact value of the sine, cosine, and tangent of each angle. 270° All Students Take Calculus Step 1 Find the reference angle. Step 2 Find the sin, cos, and tan of the reference angle. Step 3 Adjust the signs, if needed. sin 90° = 1 cos 90° = 0 tan 90° = und.

Using Reference Angles to Evaluate Trigonometric Functions Use a reference angle to find the exact value of the sine, cosine, and tangent of each angle. All Students Take Calculus Step 1 Find the reference angle. Step 2 Find the sin, cos, and tan of the reference angle. Step 3 Adjust the signs, if needed.

Using Reference Angles to Evaluate Trigonometric Functions Use a reference angle to find the exact value of the sine, cosine, and tangent of each angle. Students All Take Calculus Step 1 Find the reference angle. Step 2 Find the sin, cos, and tan of the reference angle. Step 3 Adjust the signs, if needed.

If you know the measure of a central angle of a circle, you can determine the length s of the arc intercepted by the angle.

Automobile Application A tire of a car makes 653 complete rotations in 1 min. The diameter of the tire is 0.65 m. To the nearest meter, how far does the car travel in 1 s? Step 1 Find the radius of the tire. The radius is of the diameter. Step 2 Find the angle θ in radian through which the tire rotates in 1 second. 1 rotation = 2p. Change to seconds

Automobile Application An minute hand on Big Ben’s Clock Tower in London is 14 ft long. To the nearest tenth of a foot, how far does the tip of the minute hand travel in 1 minute? Step 1 Find the radius of the clock. r =14 Step 2 Find the angle θ in radian through which the hour hand rotates in 1 minute. 1 hour = 2p. Change to minutes

Lesson 10.3 Practice B