Given that sin65^∘ ≈0.9063, cos65^∘ ≈0.4226 tan65^∘ ≈2.1445, cot65^∘ ≈0.4663 sec

step 1 In this question we have to find the six function values of 25. When we start with sine 25, we k

Given that sin65^∘ ≈0.9063, cos65^∘ ≈0.4226 ...

Given that $$\begin{aligned} &\sin 65^{\circ} \approx 0.9063, \quad \cos 65^{\circ} \approx 0.4226\\ &\tan 65^{\circ} \approx 2.1445, \quad \cot 65^{\circ} \approx 0.4663\\ &\sec 65^{\circ} \approx 2.3662, \quad \csc 65^{\circ} \approx 1.1034 \end{aligned}$$ find the six function values of $25^{\circ} .$

Given that
$$\begin{aligned}
&\sin 65^{\circ} \approx 0.9063, \quad \cos 65^{\circ} \approx 0.4226\\
&\tan 65^{\circ} \approx 2.1445, \quad \cot 65^{\circ} \approx 0.4663\\
&\sec 65^{\circ} \approx 2.3662, \quad \csc 65^{\circ} \approx 1.1034
\end{aligned}$$
find the six function values of $25^{\circ} .$

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Key Concepts

Cofunction Identities

Cofunction identities express the relationship between trigonometric functions of complementary angles; for instance, the sine of an angle is equal to the cosine of its complement. This is crucial when finding the trigonometric values of an angle by relating them to the known values of its complementary angle.

Reciprocal Identities

Reciprocal identities provide the connection between a trigonometric function and its reciprocal function. For example, secant is the reciprocal of cosine and cosecant is the reciprocal of sine. These identities are essential for computing one function if its reciprocal is known.

Relationships Among Trigonometric Functions

The basic trigonometric functions (sine, cosine, tangent, cotangent, secant, and cosecant) are interrelated; recognizing these relationships allows one to derive unknown values from known ones using identities such as tan ? = sin ?/cos ? and cot ? = cos ?/sin ?. This interconnectedness is fundamental in solving problems involving multiple trigonometric functions.

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