Answer:
cosjk = √55 i/3
tanjk = 8/√55 i
Step-by-step explanation:
Given
sin jk = 8/3
According to SOH CAH TOA
Sin theta = opposite/hypotenuse = 8/3
Opposite = 8
hypotenuse = 3
Get the adjacent using the pythagoras theorem
hyp² = opp²+adj²
adj² = hyp² - opp²
adj² = 3² - 8²
adj² = 9-64
adj² = -55
adj = √-55
adj = √55 i (i = √-1)
Get cosjk
cosjk = adj/hyp
cosjk = √55 i/3
Get tanjk
tanjk = opp/adj
tanjk = 8/√55 i
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Solve the trigonometric equation:

Restriction for the solution:

Square both sides of
(i):

![\mathsf{\dfrac{sin\,x}{cos^2\,x}\cdot \left[2\cdot (1-sin^2\,x)-sin\,x \right]=0}\\\\\\ \mathsf{\dfrac{sin\,x}{cos^2\,x}\cdot \left[2-2\,sin^2\,x-sin\,x \right]=0}\\\\\\ \mathsf{-\,\dfrac{sin\,x}{cos^2\,x}\cdot \left[2\,sin^2\,x+sin\,x-2 \right]=0}\\\\\\ \mathsf{sin\,x\cdot \left[2\,sin^2\,x+sin\,x-2 \right]=0}](https://tex.z-dn.net/?f=%5Cmathsf%7B%5Cdfrac%7Bsin%5C%2Cx%7D%7Bcos%5E2%5C%2Cx%7D%5Ccdot%20%5Cleft%5B2%5Ccdot%20%281-sin%5E2%5C%2Cx%29-sin%5C%2Cx%20%5Cright%5D%3D0%7D%5C%5C%5C%5C%5C%5C%20%5Cmathsf%7B%5Cdfrac%7Bsin%5C%2Cx%7D%7Bcos%5E2%5C%2Cx%7D%5Ccdot%20%5Cleft%5B2-2%5C%2Csin%5E2%5C%2Cx-sin%5C%2Cx%20%5Cright%5D%3D0%7D%5C%5C%5C%5C%5C%5C%20%5Cmathsf%7B-%5C%2C%5Cdfrac%7Bsin%5C%2Cx%7D%7Bcos%5E2%5C%2Cx%7D%5Ccdot%20%5Cleft%5B2%5C%2Csin%5E2%5C%2Cx%2Bsin%5C%2Cx-2%20%5Cright%5D%3D0%7D%5C%5C%5C%5C%5C%5C%20%5Cmathsf%7Bsin%5C%2Cx%5Ccdot%20%5Cleft%5B2%5C%2Csin%5E2%5C%2Cx%2Bsin%5C%2Cx-2%20%5Cright%5D%3D0%7D)
Let

So the equation becomes

Solving the quadratic equation:



You can discard the negative value for
t. So the solution for
(ii) is

Substitute back for
t = sin x. Remember the restriction for
x:

where
k is an integer.
I hope this helps. =)
Answer:
V= 18.75 cm^3
Step-by-step explanation:
- The formula for finding the volume for <em>any</em> given shape is V = L x W x H.
- So, multiply 2 1/2 cm x 2 1/2 cm x 3 cm.
- This gives you 18.75 cm^3
Answer:
Option (C)
Step-by-step explanation:
Given inequalities are,
81 > x and x > 68
Therefore, 81 > x > 68 is the inequality representing the solution area for x.
Out of x = 88, 85 and 80,
x = 80 will lie between the range of x = 68 and x = 81.
Therefore, Option (C) will be the correct option.