SOLUTION: I have three questions that I need extreme help on. 1. Find sec thata if sin theta=-4/5 and 270 degrees<theta<360 degrees. 2. Simplify: (1/sec theta + sin^2 theta/cos theta)cos

Question 172974: I have three questions that I need extreme help on.
1. Find sec thata if sin theta=-4/5 and 270 degrees 2. Simplify: (1/sec theta + sin^2 theta/cos theta)cos theta.
3. Find the exact value of: cos315 degrees.
I have to show my work to get any credit. Please help.
Thanks
Found 2 solutions by midwood_trail, solver91311:
Answer by midwood_trail(310) (Show Source): You can put this solution on YOUR website!
I will do number 3 and leave the rest to others.
3. Find the exact value of: cos315 degrees.

Cos315 lies in quadrant 4.
We need to find its reference angle.
To do so, subtract 315 degrees from 360 degrees.
Then:
360 degrees - 315 degrees = 45 degrees
The cosine of an angle is positive in quadrant 4.
The exact value of cos315 = cos45 = sqrt{2}/2
Final answer: sqrt{2}/2

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Note: I use instead of theta because theta won't render on this system.

or

so or but you need to rationalize the denominators so or

***************

2.

so:

Apply LCD of

But so:

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3. An angle of 315� is equivalent to an angle of -45� either of which is formed by a ray bisecting the right angle formed by the positive x-axis and the negative y-axis. This ray intersects the unit circle at a point that forms the vertex of an isoceles right triangle, the other two vertices being the origin and the point (,) and having a hypotenuse of length 1. The Pythagorean theorem gives us that the legs of the triangle are of length . The x coordiate of the vertex at the unit circle is positive and the y coordinate is negative because this is a Quadrant IV angle. Hence,

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