Right angled trigonometry and tan(theta)

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z jay
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#1
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#1
so this is the question from my exercise.

Question 7. Given that y = tanθ
(i) Draw and label a right angled triangle that represents this situation. Now use the diagram to:
(ii) Write an expression for sinθ in terms of y.
(iii) Write an expression for cscθ in terms of y.
(iv) Write an expression for secθ in terms of y.

so i drew the triangle and and seeing as y = opp/adj i am fairly sure that
opp = adj * y but i honestly have no clue how to write sinθ in terms of y and need a little bit of guidance with that and mainly how opp and adj and hyp are expressed in terms of y.

i have the solutions to the exercise but it just jumps straight to the answer with no working out so any guidance at all would be much appreciated, thanks.
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username1732133
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#2
Report 3 years ago
#2
(Original post by z jay)
so this is the question from my exercise.

Question 7. Given that y = tanθ
(i) Draw and label a right angled triangle that represents this situation. Now use the diagram to:
(ii) Write an expression for sinθ in terms of y.
(iii) Write an expression for cscθ in terms of y.
(iv) Write an expression for secθ in terms of y.

so i drew the triangle and and seeing as y = opp/adj i am fairly sure that
opp = adj * y but i honestly have no clue how to write sinθ in terms of y and need a little bit of guidance with that and mainly how opp and adj and hyp are expressed in terms of y.

i have the solutions to the exercise but it just jumps straight to the answer with no working out so any guidance at all would be much appreciated, thanks.
You already have opp = adj * y

The size of the triangle is unimportant so the adjacent side can be any length. Choose a nice small positive integer. You now have two sides of the triangle. Use Pythagoras' theorem to find the third side in terms of y.
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RogerOxon
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#3
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(Original post by z jay)
so this is the question from my exercise.

Question 7. Given that y = tanθ
(i) Draw and label a right angled triangle that represents this situation. Now use the diagram to:
(ii) Write an expression for sinθ in terms of y.
(iii) Write an expression for cscθ in terms of y.
(iv) Write an expression for secθ in terms of y.

so i drew the triangle and and seeing as y = opp/adj i am fairly sure that
opp = adj * y but i honestly have no clue how to write sinθ in terms of y and need a little bit of guidance with that and mainly how opp and adj and hyp are expressed in terms of y.

i have the solutions to the exercise but it just jumps straight to the answer with no working out so any guidance at all would be much appreciated, thanks.
Draw the triangle. Note that the angle remains the same regardless of the size of the triangle, so you can choose its size. I'd mark the opposite as y and the adjacent as 1. Use Pythagoras to calculate the hypotenuse.
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