Terminal point P(θ) lies on the line segment joining the origin & the indicated point. Sketch the figure and find the circular function for each real number θ (3,4)Show complete solution and...

Terminal point P(θ) lies on the line segment joining the origin & the indicated point. Sketch the figure and find the circular function for each real number θ

(3,4)

Show complete solution and explain the answer.

Asked on by spock4

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embizze | High School Teacher | (Level 1) Educator Emeritus

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(1) Draw a right triangle in the first quadrant with vertices A(0,0),B(3,4) and C(3,0). Let angle `theta` be `/_CAB` .

(2) Then AC=3,BC=4, and AC=5 (Using the pythagorean theorem or recognizing the pythagorean triplet).

AC is adjacent (adj) to `theta` , BC is opposite to `theta` (opp), and AB is the hypotenuse (hyp).

(3) Use the trigonometric ratios:

`sin theta = "opp"/"hyp"="BC"/"AB"=4/5`

`cos theta="adj"/"hyp"="AC"/"AB"=3/5`

`tan theta = "opp"/"adj"="BC"/"AC"=4/3`

`csc theta = "hyp"/"opp"="AB"/"BC"=5/4`

`sec theta = "hyp"/"adj"="AB"/"AC"=5/3`

`cot theta = "adj"/"opp"="AC"/"BC"=3/4`

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