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Hunter-Best [27]
3 years ago
5

1 + 5sin^2x= 7sin^2x solve trig equation. Can you show me how to solve this trig equation?

Mathematics
1 answer:
pantera1 [17]3 years ago
8 0

Answer: x = \frac{\pi}{4}\pm k\frac{\pi}{2}\,\,\,\,\,\,k=\{0,1,2,...\}

Step by step:

1 + 5\sin^2x= 7\sin^2x\\\sin^2 x\rightarrow z\\1 + 5z = 7z\\2z = 1\\z = \frac{1}{2}\implies \sin^2 x = \frac{1}{2}\\|\sin x| = \frac{1}{\sqrt{2}}\\\sin x = \pm\frac{1}{\sqrt{2}}=\pm\frac{\sqrt{2}}{2}\\\implies x = \frac{\pi}{4}\pm k\frac{\pi}{2}\,\,\,\,\,\,k=\{0,1,2,...\}

(Used a table of common angles)

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What is the measure of angle 3, in degrees, in the figure shown?
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Answer:

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Step-by-step explanation:

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Need help how do I do this, start it, and the steps please
Harman [31]
Let's solve this problem step-by-step.

STEP-BY-STEP SOLUTION:

Let's first write down the equation we are going to solve.

( 1 / 3 )h - 4 [ ( 2 / 3 )h - 3 ] = ( 2 / 3 )h - 6

To begin with, we will expand the brackets => [ ]

( 1 / 3 )h - ( 8 / 3 )h + 12 = ( 2 / 3 )h - 6

Next we will collect like terms by placing all the individual numbers on the right-side of the equation and the terms with ( h ) on the left-hand side of the equation so that we can begin making ( h ) the subject.

( 1 / 3 )h - ( 8 / 3 )h - ( 2 / 3 )h = - 6 - 12

Then we will simplify both the left-hand side and right-hand side of the equation to solve it for ( h ).

( - 9 / 3 )h = - 18

- 3h = - 18

h = - 18 / - 3

h = 18 / 3

h = 6

FINAL ANSWER:

Therefore, the answer is:

h = 6

Hope this helps! :)
Have a lovely day! <3
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