Question 402886: Please help me with this problem...
Find the exact values of the sine, cosine, tangent, secant, and cosecant of the angle (theta) if (theta) is in standard position and its terminal side is in the quadrant IV positioned on the line 3y + 5x = 0.
Thank You!!
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Find the exact values of the sine, cosine, tangent, secant, and cosecant of the angle (theta) if (theta) is in standard position and its terminal side is in the quadrant IV positioned on the line 3y + 5x = 0.
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3y+5x=0
change to standard form, y=mx+b
3y=-5x
y=(-5/3)x
This is a straight line thru the origin with a slope of -5/3.
Since the terminal side of angle theta is on this line, a right triangle is formed in the 4th quadrant with the x-leg=3 and the y-leg=-5. Using the pythagorean theorem, the hypotenuse calculates to sqrt(34).
Exact values of the six trig functions are as follows: (using A in place of theta)
sin A=-5/sqrt(34)
cos A=3/sqrt(34)
tan A=-5/3
cot A=-3/5
csc A=-sqrt(34)/5
sec A=sqrt(34)/3
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