The value of and can be expressed in terms of trigonometric ratios as
Further explanation:
Trigonometric functions are the real functions. In any right angle triangle there are six trigonometric functions sine, cosine, tangent, secant, cosecant, cotangent.
Given:
The right angle triangle has the sides .
Calculation:
From the attached Figure 1, we can see that the triangle is the right angle triangle.
We can apply all trigonometric ratios here.
The length of the adjacent side to the angle is and the length of the opposite side to the angle is the and the hypotenuse is .
The value of is the ratio of the side which is opposite to the angle and the adjacent side to the angle .
The value of can be mathematically expressed as follows:
Therefore, the value of can be evaluated as follows:
Further solve the above equation as follows:
Therefore, the value of in terms of trigonometric ratios is .
The value of is the ratio of the side which is adjacent to the angle and the hypotenuse of the right angle triangle.
The value of can be mathematically expressed as follows:
Therefore, the value of can be evaluated as follows:
Further solve the above equation as follows:
Therefore, the value of in terms of trigonometric ratios is .
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Answer details:
Grade: Middle school
Subject: Mathematics
Chapter: Trigonometry
Keywords: Sine, cosine, cotangent, tangent, cosecant, secant, theta, right angle triangle, adjacent side opposite side, hypotenuse, base, perpendicular.