QQuestionAnatomy and Physiology
QuestionAnatomy and Physiology
List the 6 reciprocal identities. sin 𝜃 = csc 𝜃 = cos 𝜃 = sec 𝜃 = tan 𝜃 = cot
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Answer
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Step 1:
sin heta = \frac{1}{csc heta}
The first reciprocal identity is: Explanation: The reciprocal of the cosecant of an angle is the sine of that angle.
Step 2:
csc heta = \frac{1}{sin heta}
The second reciprocal identity is: Explanation: The reciprocal of the sine of an angle is the cosecant of that angle.
Step 3:
cos heta = \frac{1}{sec heta}
The third reciprocal identity is: Explanation: The reciprocal of the secant of an angle is the cosine of that angle.
Step 4:
sec heta = \frac{1}{cos heta}
The fourth reciprocal identity is: Explanation: The reciprocal of the cosine of an angle is the secant of that angle.
Step 5:
tan heta = \frac{1}{cot heta}
The fifth reciprocal identity is: Explanation: The reciprocal of the cotangent of an angle is the tangent of that angle.
Step 6:
cot heta = \frac{1}{tan heta}
The sixth reciprocal identity is: Explanation: The reciprocal of the tangent of an angle is the cotangent of that angle.
Final Answer
- sin heta = \frac{1}{csc heta} - csc heta = \frac{1}{sin heta} - cos heta = \frac{1}{sec heta} - sec heta = \frac{1}{cos heta} - tan heta = \frac{1}{cot heta} - cot heta = \frac{1}{tan heta}
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