Iris .ir#aaEr.=2rFz E Ee Z ha - MRS. GORDON'S CLASSROOM · Now do the same thing with the triangle in the second quadrant. What is the T-coordinate? What is the U-coordinate? What

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:

2/28/19 8.4

coordinate trig

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.ir#aaEr.=2rFz=

wfp E Ee -

- Z ha ¥Opp

to Es as I. .

6Tta=f .

I =0=31539^13

. tan - ' 135-0=56.30

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.






How about the third quadrant?






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=opp

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lookout triangle on

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They are all positive

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-315csco=

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How about the fourth quadrant?






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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-9=0pp

6=adj

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Zz hyp2

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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


5. tan 𝜃 = − 25


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Iris .ir#aaEr.=2rFz E Ee Z ha - MRS. GORDON'S CLASSROOM · Now do the same thing with the triangle in the second quadrant. What is the T-coordinate? What is the U-coordinate? What