Leo asked in Science & MathematicsMathematics · 2 months ago

How do I find tan(𝜃) + sin(𝜃) for the angle 𝜃?.?

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• ?
Lv 7
2 months ago

The length of the hypotenuse

h=sqr(9^2+5^2)=sqr(106)

=>

tan(theta)+sin(theta)

=

5/9+5/sqr(106)

=

1.041198487

approximately.

• ?
Lv 7
2 months ago

tan(𝜃) + sin(𝜃)

= 5/9 + 5/sqrt 106

= 1.0411984867341877

• 2 months ago

tan(t) + sin(t) =>

tan(t) + 1/csc(t) =>

tan(t) + 1/sqrt(csc(t)^2) =>

tan(t) + 1/sqrt(1 + cot(t)^2) =>

(5/9) + 1/sqrt(1 + (9/5)^2) =>

(5/9) + 1/sqrt(1 + 81/25) =>

(5/9) + 1/sqrt((25 + 81)/25) =>

(5/9) + sqrt(25/(25 + 81)) =>

(5/9) + sqrt(25/106) =>

(5/9) + 5/sqrt(106) =>

(5/9) + 5 * sqrt(106) / 106 =>

(5 * 106 + 5 * 9 * sqrt(106)) / (9 * 106) =>

5 * (106 + 9 * sqrt(106)) / 954 =>

5 * (9 + sqrt(106)) * sqrt(106) / 954

• 2 months ago

Remember the SOH-CAH-TOA mnemonic:

SOH --> Sin(θ) = Opposite/Hypotenuse

CAH --> Cos(θ) = Adjacent/Hypotenuse

TOA --> Tan(θ) = Opposite/Adjacent

In your picture you have the Opposite side (5) and the Adjacent side (9), so tan(θ) is really easy.

tan(θ) = 5/9

For sin(θ) you need the hypotenuse. Do you remember the Pythagorean Theorem?

a² + o² = h²

9² + 5² = h²

81 + 25 = h²

106 = h²

h = √106

Now can *you* find an expression for sin(θ)? Add them together.

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• rotchm
Lv 7
2 months ago

Hint: What is tan(theta) here? [they gave it to you].

Answer that then we will take it from there.

Hopefully no one will spoil you the answer. That would be very irresponsible of them.

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