Question

suppose angle 0, in radians, is in quadrant 3 of the unit circle. if sin(0)=-0.45, what are the values of cos(0) and tan(0)?

Answer 1

Answer:

Imagine a right triangle being drawn on the cartesian plane, as in the following example.



Since sin = opposite/hypotenuse, the side opposite to θ is 3 and the hypotenuse is 8, we can rearrange our pythagorean theorem to find the adjacent side, b.

a2+b2=c2

b2=c2−a2

b2=82−32

b2=64−9

b2=55

b=−√55

So, now we know that the adjacent side measures −√55 units (since the x axis is negative in quadrant II) in length. Thus we can deduce that cosθ=−√558 and tanθ=−3√55

Now, for cscθ,secθandcotθ, we must apply the reciprocal identities.

cscθ=1sinθ

secθ=1cosθ

cotθ=1tanθ

Therefore, cscθ=83,secθ=−8√55andcotθ=−

Answer 2

If the value of the angle θ is 243.26°. Then the value of cos(θ) and tan(θ) will be -0.4499 and 1.9848.

What is trigonometry?

Trigonometry deals with the relationship between the sides and angles of a right-angle triangle.

Suppose angle θ, in radians, is in quadrant 3 of the unit circle.

If sin(θ) = - 0.45, then the values of cos(θ) and tan(θ) will be

sin(θ) = - 0.45

Then the value of the angle θ will be

$\rm \theta = \sin ^{-1} (-0.05)\\\\\theta = -26.74 \ (counter\ clockwise)$

Then the value of angle θ from the first quadrant, we have

$\rm \theta = -26.74 +270\\\\\theta = 243.26$

Then the value of cos(θ) and tan(θ) will be

$\cos 243.26 ^o = -0.4499$

$\tan 243.26 = 1.9848$

More about the trigonometry link is given below.

https://brainly.com/question/22698523

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