Given that $sin θ cos θ = \frac{7}{50}$ $sin theta cos theta =7/50$ and $0^{0} < θ < 90^{0}$ $0^0 < theta < 90^0$ . Find the value of $cos θ$ $cos theta$ .?

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Given that $sin θ cos θ = \frac{7}{50}$ $sin theta cos theta =7/50$ and $0^{0} < θ < 90^{0}$ $0^0 < theta < 90^0$ . Find the value of $cos θ$ $cos theta$ .?

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Answer 1 · 2018-06-22T14:10:47

$\frac{7}{5 \cdot \sqrt{2}}, \frac{1}{5 \cdot \sqrt{2}}$ $7/(5*sqrt(2)),1/(5*sqrt(2))$

Explanation:

Solving the equation
$sin (θ) \cdot cos (θ) = \frac{7}{50}$ $sin(theta)*cos(theta)=7/50$
in the given interval we get

$x_{1} = - 2 arctan (7 - 5 \sqrt{2})$ $x_1=-2arctan(7-5sqrt(2))$

$x_{2} = 2 arctan (\frac{1}{7} (5 \sqrt{2} - 1))$ $x_2=2arctan(1/7(5sqrt(2)-1))$
so we gat

$cos (x_{1}) = \frac{7}{5 \sqrt{2}}$ $cos(x_1)=7/(5sqrt(2))$

$cos (x_{2}) = \frac{1}{5 \sqrt{2}}$ $cos(x_2)=1/(5sqrt(2))$

Answer 2 · 2018-06-22T14:33:16

$8^{\circ} 13, 81^{\circ} 87$ $8^@13, 81^@87$

Explanation:

$sin t . cos t = \frac{7}{50}$ $sin t.cos t = 7/50$
Use trig identity: sin 2t = 2sin t.cos t
In this case:
$sin t . cos t = \frac{sin 2 t}{2} = \frac{7}{50}$ $sin t.cos t = (sin 2t)/2 = 7/50$
$sin 2 t = \frac{15}{50} = \frac{7}{25}$ $sin 2t = 15/50 = 7/25$
Calculator and unit circle give 2 solutions for 2t:
$2 t = 16^{\circ} 26$ $2t = 16^@26$ , and $2 t = 180 - 16.26 = 163^{\circ} 74$ $2t = 180 - 16.26 = 163^@74$
a. 2t = 16.26 + k360
$t = 8^{\circ} 13 + k 180^{\circ}$ $t = 8^@13 + k180^@$
b. 2t = 163.74 + k360
$t = 81^{\circ} 87 + k 180^{\circ}$ $t = 81^@87 + k180^@$
Answers for (0, 90)
$8^{\circ} 13, 81^{\circ} 87$ $8^@13, 81^@87$
cos (8.13) = 0.99
cos (81.87) = 0.14

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Given that $sin θ cos θ = \frac{7}{50}$ $sin theta cos theta =7/50$ and $0^{0} < θ < 90^{0}$ $0^0 < theta < 90^0$ . Find the value of $cos θ$ $cos theta$ .?

Help pls...

2 Answers

Explanation:

Explanation:

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Given that sin theta cos theta =7/50sinθcosθ=750sin theta cos theta =7/50 and 0^0 < theta < 90^000<θ<9000^0 < theta < 90^0. Find the value of cos thetacosθcos theta.?

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Explanation:

Explanation:

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Given that $sin θ cos θ = \frac{7}{50}$ $sin theta cos theta =7/50$ and $0^{0} < θ < 90^{0}$ $0^0 < theta < 90^0$ . Find the value of $cos θ$ $cos theta$ .?