Question 1174405: 1.Given: cos theta = 5/13, theta is in quadrand I. Find:tan theta.
2.Given:sin theta=1/3,theta is in quadrand II. Find:cos theta.
3.Given:tan theta =2/3 theta is in quadrand IV. Find:sin theta.
4.Given:sec theta=9/8,theta is in quadrand III . Find:csc theta.
5.Given:csc theta= 2, sec theta < 0. Find tan theta.
6:Given:cot theta= 8/15, sin theta < 0.find cos theta.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 1.Given: cos theta = 5/13, theta is in quadrant I. Find:tan theta.
arccos(5/13) = 67.38013505 degrees.
that's in quadrant 1.
equivalent angle in quadrant 1 is the same.
tan(67.38013505) = 2.4
2.Given:sin theta=1/3,theta is in quadrant II. Find:cos theta.
arcsin(1/3) = = 19.47122063 degrees.
that's in quadrant 1.
equivalent angle in quadrant 2 is 180 minus that = 160.5287794.
cos(that) = -.9428090416.
cosine function is negative in quadrant 2.
3.Given:tan theta = 2/3 theta is in quadrant IV. Find:sin theta.
arctan(2/3) = 33.69006753 degrees.
that's in quadrant 1.
equivalent angle in quadrant 4 is 360 minus that = 326.3099325.
sin(that) = -.5547001962.
sine function is negative in quadrant 4.
4.Given:sec theta=9/8,theta is in quadrant III . Find:csc theta.
sec(theta) = 1/cos(theta), therefore:
since secant = 1/cosine, then:
1/cos(theta) = 9/8.
solve for cos(theta) to get cos(theta) = 1/(9/8) = 8/9.
arccos(8/9) = 27.26604445 degrees.
that's in quadrant 1.
equivalent angle in quadrant 3 is 180 plus that = 207.2660445
csc(that) = 1/sin(that) = -2.182820625.
cosecant is negative in third quarter because cosecant = 1/sine and sine is negative in quadrant 3.
5.Given:csc theta= 2, sec theta < 0. Find tan theta.
csc(theta) = 1/sin(theta).
solve for sin(theta) to get sin(theta) = 1/2.
arcsin(1/2) = 30 degrees.
that's in quadrant 1.
sec(theta) is smaller than 0.
sec(theta) is equal to 1/cos(theta) and is negative in quadrants 2 and 3.
the equivalent angle in quadrant 2 is 180 - 30 = 150 degrees.
tan(150) = -.5773502692.
tangent function is negative in quadrant 2.
the equivalent angle in quadrant 3 is 180 + 30 = 210 degrees.
tan(210) = .5773502692.
the tangent function is positive in quadrant 3.
this is because sine is negative and cosine is negative in quadrant 3 and tangent = sin/cos = negative/negative = positive in quadrant 3.
it's the same value as in quadrant 2 only it's negative in quadrant 2 and positive in quadrant 3.
6:Given:cot theta= 8/15, sin theta < 0.find cos theta.
cot(theta) = 1/tan(theta) = 8/15
solve for tan(theta) to get tan(theta) = 15/8.
arctan(15/8) = 61.92751306 degrees.
that's in quadrant 1.
sin(theta) is negative in quadrant 3 and 4.
equivalent angle in quadrant 3 is 180 plus that = 241.9275131 degrees.
cos(that) = -.4705882353.
cosine is negative in quadrant 3.
equivalent angle in quadrant 4 is 360 minus that = 298.0724869 degrees.
cos(that) = .4705882353.
cosine is positive in quadrant 4.
if you are confused or have any questions about any of this, let me know and i'll explain as best i can.
theo
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