SOLUTION: If sin(x) = − 20 29 and x is in quadrant III, with 0° ≤ x < 360°, find the exact values of the expressions without solving for x. (a) sin x 2 (b)

Question 1204627: If
sin(x) = −
20
29
and x is in quadrant III, with 0° ≤ x < 360°, find the exact values of the expressions without solving for x.
(a)
sin
x
2

(b)
cos
x
2

(c)
tan
x
2

Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
If
and is in quadrant III, with °, find the exact values of the expressions without solving for .

in Q III both sin and cos are
we also know that

solve for

substitute given value of

or
we need

(a) use Half-Angle Identities

or
in Q III

(b)

or
in Q III

(c)

or
In the third quadrant, the values for tan are only.

Answer by ikleyn(52806) (Show Source): You can put this solution on YOUR website!
.

In the post by @MathLover1, her answer to (a), = , is incorrect. To determine the correct answer, we should analyze in which quadrant the angle lies. Since angle x is in QIII, we conclude that lies in QII. Hence, must be POSITIVE in this problem. THEREFORE, the correct answer to (a) is = , the opposite number to the answer by @MathLover1. Similarly, in her post, the answer to (c), = , is incorrect. Again, the angle lies in QII, where tangent is always negative. THEREFORE, the correct answer to (c) is = , the opposite number to the answer by @MathLover1.

--------------------

Hello, could you take care about your posts, in order for they come in good format ?

For it, you should STOP copy-paste from your source, since it does not work properly.

You should print your posts manually using your keyboard and supporting the rules of mathematical grammar.

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