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Trig identities

now sure where to start.
I did 6(1-sin^2 x) = tan(x)cos(x) +4 so farScreenshot 2020-04-25 at 19.33.46.png
Tan = sin / cos
So tan cos = sin
Use C^2 + S^2 = 1 to rewrite cos2 in terms of sin
Simplify and rearra
Original post by mathsprobelmssss
now sure where to start.
I did 6(1-sin^2 x) = tan(x)cos(x) +4 so farScreenshot 2020-04-25 at 19.33.46.png


All what you need are the definitions and formulas above in post #2 to convert and put them in the equation to solve step by step:

tan = sin/cos <=> sin = tan*cos

cos^2 + sin^2 = 1 <=> cos^2 = 1 - sin^2

The rest should be a peace of cake for you.

EDIT: After Muttley79 request, I remove the spoiler.
(edited 3 years ago)
Original post by Kallisto
I am writing on Smartphone, so I hope that you can see my solutions in the spoiler. All what you need are the definitions and formulas above to convert and put in the equation to solve step by step.


Spoiler



Screenshot 2020-04-26 at 13.11.28.pngim not sure how to start off part b
Original post by mathsprobelmssss
Screenshot 2020-04-26 at 13.11.28.pngim not sure how to start off part b


You can find what all the points are by solving the equation, then write them on the graph and think about it visually.
Original post by mathsprobelmssss
Screenshot 2020-04-26 at 13.11.28.pngim not sure how to start off part b


Its where the graph of 6cos^2(theta) is above the graph of tan(theta)cos(theta)+4.

Clearly, these regions are inbetween points of intersection. So you should first determine the points of intersection, and label their x coords on the diagram to aid you.
Original post by Dancer2001
You can find what all the points are by solving the equation, then write them on the graph and think about it visually.

how would I solve the equations? for the cos graph I multiplied the range by 6 so 0<x<2160
Original post by mathsprobelmssss
how would I solve the equations? for the cos graph I multiplied the range by 6 so 0<x<2160


You find the points where two lines intersect by solving the equations simultaneously. In this example it means putting them equal to each other, so you can use your answer to part a. Part a is a quadratic, so you should be able to solve it (use a substitution if it helps you). This will give you the x coordinate of the points.
Original post by Dancer2001
You find the points where two lines intersect by solving the equations simultaneously. In this example it means putting them equal to each other, so you can use your answer to part a. Part a is a quadratic, so you should be able to solve it (use a substitution if it helps you). This will give you the x coordinate of the points.

I got 1/2 and -2/3.
I then did inverse sin (1/2) and got 30.
Original post by Kallisto
I am writing on Smartphone, so I hope that you can see my solutions in the spoiler. All what you need are the definitions and formulas above to convert and put in the equation to solve step by step.


Please remove the spoiler - it is against the rules to post solutions. We are asked to give hints :smile:
Original post by mathsprobelmssss
I got 1/2 and -2/3.
I then did inverse sin (1/2) and got 30.


30 will be the first point, can you find the others?
Original post by Dancer2001
30 will be the first point, can you find the others?

I got 30,150,210 and 330
Original post by Muttley79
Please remove the spoiler - it is against the rules to post solutions. We are asked to give hints :smile:


Did it. Sorry, I did not know that it is against the rules, have removed the spoiler, the way better now?

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