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tan = sin/cos

Now cos2 = 1 - sin2 so cos = +/- sqrt(1 - sin2)

In the second quadrant, cos is negative, so cos = - sqrt(1 - sin2)

So that tan = sin/[-sqrt(1 - sin2)]

or -sin/sqrt(1 - sin2)

Q: What is tan theta in terms of sin theta in quadrant II?

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The identity for tan(theta) is sin(theta)/cos(theta).

(in a past paper it asks u to solve this for -180</=theta<180, so I have solved it) Tan theta =-1, so theta = -45. Use CAST diagram to find other values of theta for -180</=theta<180: Theta (in terms of tan) = -ve, other value is in either S or C. But because of boundaries value can only be in S. So other value= 180-45=135. Do the same for sin. Sin theta=2/5 so theta=23.6 CAST diagram, other value in S because theta (in terms of sin)=+ve. So other value=180-23.6=156.4.

'csc' = 1/sin'tan' = sin/cosSo it must follow that(cos) (csc) / (tan) = (cos) (1/sin)/(sin/cos) = (cos) (1/sin) (cos/sin) = (cos/sin)2

Almost by definition, tan Î¸ = sin Î¸ / cos Î¸ You can convert this to sine Î¸ in several ways, for example: sin Î¸ / cos Î¸ = sin Î¸ / cos (pi/2 - Î¸) Or here is another way, using the Pythagorean identity: sin Î¸ / cos Î¸ = sin Î¸ / root(1 - sin2Î¸)

The expression tan(theta) sin(theta) / cos(theta) simplifies to sin^2(theta) / cos(theta). In trigonometry, sin^2(theta) is equal to (1 - cos^2(theta)), so the expression can be further simplified to (1 - cos^2(theta)) / cos(theta).

Related questions

0.75

Since sin(theta) = 1/cosec(theta) the first two terms simply camcel out and you are left with 1 divided by tan(theta), which is cot(theta).

If tan(theta) = x then sin(theta) = x/(sqrt(x2 + 1) so that csc(theta) = [(sqrt(x2 + 1)]/x = sqrt(1 + 1/x2)

The identity for tan(theta) is sin(theta)/cos(theta).

Cotan(theta) is the reciprocal of the tan(theta). So, cot(theta) = 1/2.

Remember that tan = sin/cos. So your expression is sin/cos times cos. That's sin(theta).

No, they cannot all be negative and retain the same value for theta, as is shown with the four quadrants and their trigonemtric properties. For example, in the first quadrant (0

The value of tan and sin is positive so you must search quadrant that tan and sin value is positive. The only quadrant fill that qualification is Quadrant 1.

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The third quadrant.

(in a past paper it asks u to solve this for -180</=theta<180, so I have solved it) Tan theta =-1, so theta = -45. Use CAST diagram to find other values of theta for -180</=theta<180: Theta (in terms of tan) = -ve, other value is in either S or C. But because of boundaries value can only be in S. So other value= 180-45=135. Do the same for sin. Sin theta=2/5 so theta=23.6 CAST diagram, other value in S because theta (in terms of sin)=+ve. So other value=180-23.6=156.4.