Question

Trig identity question.....

Write the first expression in terms of the second if the terminal point determined by t is in the given quadrant.

sin t, sec t; Quadrant IV

Answer 1

In quadrant IV, sin is negative and cosine is positive. secant is the reciprocal of cosine so is also positive. The pertinent Pythagorean identity is \[\sin^2{t} = 1-\cos^2{t}\]Which is equal to \[1-\frac{1}{\sec^2{t}}\]
We can take the square root to get sin(t), but we should add the negative sign because of the quadrant:
\[\sin{t}=-\sqrt{1-\frac{1}{\sec^2{t}}}\]

Answer 2

thank you for explaining and not just an answer....
may have two more......
just going to try and work them out myself first.

Answer 3

Good luck

Answer 4

I should mention that we would have the same result in Quadrant III because it doesn't really matter what the sign of sec(t) is, just the sin(t).

Answer 5

here's another..
Write the first expression in terms of the second if the terminal point determined by t is in the given quadrant.
tan t, cos t; Quadrant III
I got \[\tan ^{2}t=1-\sin ^{2}t/\cos ^{2}t\]
but says its wrong. am i just missing a negative sign?