Trig Exact Values 2
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Question 1 of 4
1. Question
Find the exact value of:sin(-210)°Write fractions in the format “a/b”- (1/2)
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Trigonometric Functions
sinθ=oppositehypotenusecosθ=adjacenthypotenusetanθ=oppositeadjacentPositive Values in the Unit Circle
Quadrant I: AllQuadrant II: Sine onlyQuadrant III: Tangent onlyQuadrant IV: Cosine onlyFirst, draw in the ray of -210°.A negative angle goes anti-clockwise.Next, get the acute angle (θ’) for -210°.The acute angle is an angle less than 90° and is relative to the horizontal axis.Based on this diagram, simply subtract 180° from 210° to get the acute angle.θ’ = 210°-180° = 30° Finally, we can get the exact value of sin(-210)° by solving for sin30° using Exact Triangle Ratios.Note that the value is positive because Sine is positive on Quadrant II.sin(-210)° = sin30° = oppositehypotenuse = 12 12 -
Question 2 of 4
2. Question
Find the exact value of:cos495°- 1.
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Trigonometric Functions
sinθ=oppositehypotenusecosθ=adjacenthypotenusetanθ=oppositeadjacentPositive Values in the Unit Circle
Quadrant I: AllQuadrant II: Sine onlyQuadrant III: Tangent onlyQuadrant IV: Cosine onlyFirst, draw in the ray of 495°.Since the angle is greater than 360°, it makes a full revolution. To draw the ray, we must first subtract 360°.495°-360°=135°Next, get the acute angle (θ’) for 495°.The acute angle is an angle less than 90° and is relative to the horizontal axis.Based on this diagram, simply subtract 135° from 180° to get the acute angle.θ’ = 180°-135° = 45° Now, identify if cosine is positive or negative in the quadrant where the ray lies, Quadrant II.The cosine value is negative in Quadrant II.Finally, we can get the exact value of cos495° by solving for -cos45° using Exact Triangle Ratios.cos495° = -cos45° = −adjacenthypotenuse = −1√2 -1√2 -
Question 3 of 4
3. Question
Find the exact value of:tan150°-
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Chapters- Chapters
Trigonometric Functions
sinθ=oppositehypotenusecosθ=adjacenthypotenusetanθ=oppositeadjacentPositive Values in the Unit Circle
Quadrant I: AllQuadrant II: Sine onlyQuadrant III: Tangent onlyQuadrant IV: Cosine onlyFirst, draw in the ray of 150°.Next, get the acute angle (θ’) for 150°.The acute angle is an angle less than 90° and is relative to the horizontal axis.Based on this diagram, simply subtract 150° from 180° to get the acute angle.θ’ = 180°-150° = 30° Finally, we can get the exact value of tan150° by solving for -tan30° using Exact Triangle Ratios.Note that the value is negative because tangent is negative in Quadrant II.tan150° = -tan30° = −oppositeadjacent = −1√3 -1√3 -
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Question 4 of 4
4. Question
Find the exact value of:cos315°-
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Hint
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Need TextPlayCurrent Time 0:00/Duration Time 0:00Remaining Time -0:00Stream TypeLIVELoaded: 0%Progress: 0%0:00Fullscreen00:00MutePlayback Rate1x- 2x
- 1.5x
- 1.25x
- 1x
- 0.75x
- 0.5x
Subtitles- subtitles off
Captions- captions off
- English
Chapters- Chapters
Trigonometric Functions
sinθ=oppositehypotenusecosθ=adjacenthypotenusetanθ=oppositeadjacentPositive Values in the Unit Circle
Quadrant I: AllQuadrant II: Sine onlyQuadrant III: Tangent onlyQuadrant IV: Cosine onlyFirst, draw in the ray of 315°.Next, get the acute angle (θ’) for 315°.The acute angle is an angle less than 90° and is relative to the horizontal axis.Based on this diagram, simply subtract 315° from 360° to get the acute angle.θ’ = 360°-315° = 45° Finally, we can get the exact value of cos315° by solving for cos45° using Exact Triangle Ratios.Note that the value is positive because cosine is positive on Quadrant IV.cos315° = cos45° = adjacenthypotenuse = 1√2 1√2 -
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Quizzes
- Converting Angle Measures 1
- Converting Angle Measures 2
- Converting Angle Measures 3
- Finding the Central Angle in a Circle
- Finding Areas in a Circle
- Values on the Unit Circle
- Finding Missing Angles Using the Unit Circle
- Trigonometric Ratios in the Unit Circle
- Trig Exact Values 1
- Trig Exact Values 2
- Trig Equations
- Derivative of a Trigonometric Function 1
- Derivative of a Trigonometric Function 2
- Derivative of a Trigonometric Function 3
- Applications of Differentiation
- Integral of a Trigonometric Function 1
- Integral of a Trigonometric Function 2
- Applications of Integration
- Graphing Trigonometric Functions 1
- Graphing Trigonometric Functions 2
- Graphing Trigonometric Functions 3
- Graphing Trigonometric Functions 4