Find the values of sine and cosine for an angle of 45 degrees in the unit circle
First, recall that in the unit circle, an angle of 45 degrees corresponds to
From trigonometric identities:
Therefore, the values are:
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Find the values of sine and cosine for an angle of 45 degrees in the unit circle
First, recall that in the unit circle, an angle of 45 degrees corresponds to
From trigonometric identities:
Therefore, the values are:
Find the values of sin, cos, and tan at 45 degrees on the unit circle
To find the values of
The coordinates of the point on the unit circle at
Therefore, the values are:
Find the cosine of a point on the unit circle in the complex plane
Given a point on the unit circle in the complex plane, represented by the complex number
Since
Thus, the real part of
Hence, if
Find the exact values of sine, cosine, and tangent for the angle that corresponds to the point where the terminal side of angle ฮธ intersects the unit circle at (cosฮธ, sinฮธ) Given that ฮธ is in the fourth quadrant and the point on the unit circle is (1/2,
Given that
First, we recognize that
To find
Therefore, the values are:
Find the sine, cosine, and tangent of 45 degrees on the unit circle
We know that at
Therefore,
To find
Find the sine and cosine of the angle ฮธ when it equals ฯ/4 on the unit circle
To find the sine and cosine of the angle
The unit circle has a radius of 1, and for
Therefore,
Find the Cartesian coordinates of a point on the unit circle when given an angle and a trigonometric function value
Given the angle
Since the unit circle has a radius of 1, we use the trigonometric identities for sine and cosine:
For
Therefore, the Cartesian coordinates are:
Find the sine, cosine, and tangent of a point on the unit circle
For the point on the unit circle corresponding to the angle
Step 1: Recognize that on the unit circle, the radius is 1.
Step 2: Use the angle
Step 3: Find sine and cosine for
Step 4: Calculate tangent using
Answers:
Find the value of sec(ฮธ) when ฮธ = ฯ/4 on the unit circle
To find the value of
At
Therefore,
Find the sine, cosine, and tangent values for a 45-degree angle on the unit circle
First, we need to convert the angle from degrees to radians. Since
Next, we use the unit circle values for
The tangent value is the sine value divided by the cosine value:
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