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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)
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What is the identity for tan theta?
The identity for tan(theta) is sin(theta)/cos(theta).
How do you simplify bracket 1 plus tan theta bracket bracket 5 sin theta -2 bracket equals 0?
(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.
How do you simplify cos theta times csc theta divided by tan theta?
'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
What is tan theta in terms of sin theta?
Almost by definition, tan θ = sin θ / cos θ You can convert this to sine θ in several ways, for example: sin θ / cos θ = sin θ / cos (pi/2 - θ) Or here is another way, using the Pythagorean identity: sin θ / cos θ = sin θ / root(1 - sin2θ)
Why tan theta sin theta divided by cos theta?
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).
If sin theta equals 3/4 and theta is in quadrant II what is the value of tan theta?
0.75
How do you simplify sin theta times csc theta divided by tan theta?
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).
How do you get the csc theta given tan theta in quadrant 1?
If tan(theta) = x then sin(theta) = x/(sqrt(x2 + 1) so that csc(theta) = [(sqrt(x2 + 1)]/x = sqrt(1 + 1/x2)
What is the identity for tan theta?
The identity for tan(theta) is sin(theta)/cos(theta).
If tan Theta equals 2 with Theta in Quadrant 3 find cot Theta?
Cotan(theta) is the reciprocal of the tan(theta). So, cot(theta) = 1/2.
How do you simplify tan theta cos theta?
Remember that tan = sin/cos. So your expression is sin/cos times cos. That's sin(theta).
Is it possible for sin theta cos theta and tan theta to all be negative for the same value of 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
Tan equals 0.3421 sin equals 0.3237 Which quadrant does it terminate?
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.
Sin theta 0 and tan theta 0?
4
How do you find tan-theta when sin-theta equals -0.5736 and cos-theta is greater than 0?
-0.5736
Which quadrant would an answer be in if tan was positive and sin was negative?
The third quadrant.
How do you simplify bracket 1 plus tan theta bracket bracket 5 sin theta -2 bracket equals 0?
(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.
