Finding the Exact Value
Give the exact value of the expression without using a calculator.
\[
\cos \left(\tan ^{-1} \frac{4}{3}-\tan ^{-1}\left(-\frac{8}{15}\right)\right)
\]
\[
\cos \left(\tan ^{-1} \frac{4}{3}-\tan ^{-1}\left(-\frac{8}{15}\right)\right)=
\]
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)
Finding the Value Using the Unit Circle
Find the value of \( \sin(330^\circ) \) using the unit circle
Expanding Trigonometric Expressions
Perform the indicated operation and simplify the result so that there are no quotients.
\[
(5+\sin t)^{2}+\cos ^{2} t
\]
The simplified form, with no quotients, of $(5+\sin t)^{2}+\cos ^{2} t$ is (Do not factor.)
Expanding Using Double-Angle Formulas
Rewrite $\sin \left(2 \tan ^{-1} u\right)$ as an algebraic expression in $u$.
\[
\sin \left(2 \tan ^{-1} u\right)=
\]
Expanding Using Triple-Angle Formulas
Simplify the expression \(2\sin(3x)\)
Expanding Using Sum/Difference Formulas
Use a sum or difference formula to find the exact value of the following.
\[
\sin \frac{29 \pi}{42} \cos \frac{\pi}{7}+\cos \frac{29 \pi}{42} \sin \frac{\pi}{7}
\]
Simplify Using Pythagorean Identities
The expression below simplifies to a constant, a single function, or a power of a function. Use fundamental identities to simplify the expression.
\[
\frac{\cos ^{2} x}{\sin ^{2} x}+\csc x \sin x
\]
\[
\frac{\cos ^{2} x}{\sin ^{2} x}+\csc x \sin x=
\]
Simplify by Converting to Sine/Cosine
MWF
Armando Ramirez
This quizz 5 point(s) possible
This question: 1 point(s) possible
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The expression $\frac{\cos x-\sin ^{2} x}{\cos x} \cdot \csc x$ is to be the left hand side of an equation that is an identity. Which one of the following four expressions can be used as the right hand side of the equation to complete the identity?
Inverting Trigonometric Expressions
Write the expression as an algebraic (nontrigonometric) expression in $u$, for $u>0$.
\[
\csc \left(\operatorname{arccot} \frac{\sqrt{4-u^{2}}}{u}\right)
\]
\[
\csc \left(\operatorname{arccot} \frac{\sqrt{4-u^{2}}}{u}\right)=
\]
Finding the Trig Value of an Angle
Write the expression as a single function of $\alpha$.
\[
\cos \left(0^{\circ}+\alpha\right)
\]
Choose the correct answer below.
A. $-\cos \alpha$
B. $\cos \alpha$
C. $-\sin \alpha$
D. $\sin \alpha$
Expanding Using De Moivre's Theorem
Expand the expression \((1 + i\sqrt{3})^6\) using De Moivre's theorem.