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Date: Section:
Objective:
Review: Find the exact values of all 6 trigonometric functions. Write answer in simplest form.
sin A = cos A = tan A = sec A = csc A = cot A =
Find the degree measure of 𝜃 in the above triangle.
Vocabulary:
Standard position:
Initial side:
Terminal side:
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angle is on origin t initial side is on
positive side of X-axis
starting side of angle
ending side of angle
What if I put the above triangle in standard position in the first quadrant?
What is the 𝑥-coordinate?
What is the 𝑦-coordinate?
What is the hypotenuse?
What are the 6 trig functions?
What do you notice about the signs of the 𝑥- and 𝑦-corrodinates and the 6 trig functions?
Now do the same thing with the triangle in the second quadrant.
What is the 𝑥-coordinate?
What is the 𝑦-coordinate?
What is the hypotenuse?
What are the 6 trig functions?
What do you notice about the signs of the 𝑥- and 𝑦-corrodinates and the 6 trig functions?
How about the third quadrant?
What is the 𝑥-coordinate?
What is the 𝑦-coordinate?
What is the hypotenuse?
What are the 6 trig functions?
What do you notice about the signs of the 𝑥- and 𝑦-corrodinates and the 6 trig functions?
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How about the fourth quadrant?
What is the 𝑥-coordinate?
What is the 𝑦-coordinate?
What is the hypotenuse?
What are the 6 trig functions?
What do you notice about the signs of the 𝑥- and 𝑦-corrodinates and the 6 trig functions?
What side does the 𝑥-coordinate equal on a right triangle with 𝜃 at the origin?
What side does the 𝑦-coordinate equal on a right triangle with 𝜃 at the origin?
Write the 6 trig functions using 𝑥, 𝑦, ℎ instead of opposite, adjacent, hypotenuse.
A way to remember which trig functions are positive in each quadrant:
Examples:
Find the exact values of sin 𝜃, cos 𝜃, tan 𝜃, csc 𝜃, sec 𝜃, and cot 𝜃 where 𝜃 is an angle in standard position whose terminal side contains the given point. Write answers in simplest form.
1. (−1, 3) sin 𝜃=_____________ csc 𝜃=_____________
cos 𝜃=_____________ sec 𝜃=_____________
tan 𝜃=_____________ cot 𝜃=_____________
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Students All
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Find the degree of the angle (round to the nearest tenth of a degree), in standard position, whose terminal side contains the given point.
2. (3, 8)
𝜃 = ______________________________
REMEMBER: There are 2 quadrants where each trig function is positive and 2 quadrants where each trig function is negative.
Draw the two triangles for the trig functions and find the coordinates that go with it. There will be 2 answers. Leave answers in simplest radical form. (Remember All Students Take Calculus). Then find the angles from [0, 360°) in standard position (round to the nearest tenth of a degree).
3. sin 𝜃 = − 27
Coordinates: _________ and ________ Angles: __________ and __________
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4. csc 𝜃 = 2524
Coordinates: _________ and ________ Angles: __________ and __________
5. tan 𝜃 = − 25
Coordinates: _________ and ________ Angles: __________ and __________
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