Topic
Q:
21.10. Знайдіть усі корені рівняння \( \cos \left(x+\frac{\pi}{12}\right)=-\frac{1}{2} \), які задо-
вольняють нерівність \( -\frac{\pi}{6}<x<4 \pi \).
Q:
4.2. If \( \mathrm{A}=38.6^{\circ} \) and \( \mathrm{B}=141.4^{\prime \prime} \), evaluate the following and round off your answer to 2 decimal
places.
\( 4.2 .1 \quad \cos 2 A-\sin \left(\frac{1}{2} B\right) \)
\( 4.2 .2 \quad 2 \tan ^{2} \mathrm{~B} \)
Q:
4.2. If \( \mathrm{A}=38.6^{\circ} \) and \( \mathrm{B}=141.4^{\circ} \), evaluate the following and round off your answer to 2 decimal
places.
\( \begin{array}{ll}4.2 .1 & \cos 2 A-\sin \left(\frac{1}{2} B\right) \\ 4.2 .2 & 2 \tan ^{2} B\end{array} \)
Q:
ешите уравнения:
1. \( \cos x-\cos x-2=0 \)
2. \( \cos x(\operatorname{tg} x-1)=0 \)
Q:
ешите уравнения:
1. \( \cos 2 x-\cos x-2=0 \)
2. \( \cos x(\operatorname{tg} x-1)=0 \)
3. \( 2 \sin ^{2} x+3 \cos x-3=0 \)
4. \( 2 \sin x-3 \cos x=0 \)
5. \( \cos ^{2} x+\sin x * \cos x-1=0 \)
6. \( \sin ^{2} x-10 \sin x * \cos x+21 \cos ^{2} x=0 \)
7. \( 9 \sin ^{2} x+25 \cos ^{2} x+32 \sin x * \cos x=25 \)
Q:
12 Demontrer les égalités suivantes :
(1) \( (\sin x-\cos x)^{2}=1-2 \sin x \cos x \)
(2) \( (\sin x-\cos x)(1+\sin x \cos x)=\sin ^{3} x-\cos ^{3} x \)
(3) \( \sin ^{4} x-\cos ^{4} x=1-\cos ^{2} x \)
(4) \( \frac{\sin x}{1+\cos x}=\frac{1-\cos x}{\sin x} \)
(5) \( (\cos x+\sin x)^{2}-(\cos x-\sin x)^{2}=4 \sin x \cos x \)
(6) \( \sin ^{4} x+\sin ^{2} x=\cos ^{4} x-3 \cos ^{2} x+2 \)
Q:
Solve the equation for solutions over the interval \( \left[0^{\circ}, 360^{\circ}\right. \) ).
\( 2 \cos \theta+3=-\sec \theta \)
Select the correct choice below and, if necessary, fill in the answer box to complete
A. The solution set is \( \{\square \).
(Type your answer in degrees. Dchot include the degree symbol in your ans
Q:
16. A 20 -foot high ladder reaches a tree limb when it leans at a \( 71^{\circ} \) angle
with the ground. Approximately how high is the tree limb?
20 ft
18.9 ft
15.9 ft
13.8 ft
None of these answers are correct.
Q:
17. If \( \sin \theta=\frac{3}{8} \), calculate \( \tan \theta, * \)
*Round your answer up to four decimal places.
\( \tan \theta= \)
Q:
Use an identity to solve the equation on the interval \( [0,2 \pi) \)
\[ \sin ^{2} x-6 \boldsymbol{\operatorname { c o s }} x+6=0 \]
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