HG U5D7 Sine & Cosine Relationships Oct22

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Select all the true equations:

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Write 1 equation using sine and 1 equation using cosine based on triangle 𝐴𝐵𝐶.

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Explore with Technology!
What value of 𝜃 makes this equation true? 
sin(30) = cos (𝜃)
𝜃 = _______ degrees

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Solve for a and x. Round to the nearest tenth.
a = _______  and   x = _______ 

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Solve for b and y. Round to the nearest tenth.
b = _______    and     y = _______ 
Notice anything?

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Solve for c and z. Round to the nearest tenth.
c = _______    and    z = _______ 

Notice anything?
50o + 40o = _______o        (check the others)

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Draw a diagram that will help you explain why sin(𝜃) = cos (90 − 𝜃).

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Explain why sin(𝜃) = cos (90 − 𝜃).

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Find a value for 𝜃 where sin(𝜃) < cos(𝜃).
𝜃 = _______o 

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Find a value for 𝜃 where sin(𝜃) = cos(𝜃).
𝜃 = _______o 

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Find a value for 𝜃 where sin(𝜃) > cos(𝜃).
𝜃 = _______o 

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Use your knowledge of the relationship between trigonometric ratios to answer each of the following questions.
Select all the true equations.

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Write 2 expressions that can be used to find the value of 𝑥.

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Who is correct?
Andre and Mai are discussing how to solve for side 𝐴𝐵. Andre thinks he can use the equation tan(12) = 𝑥/6 to solve for 𝐴𝐵. Mai thinks she can use the equation tan(78) = 6/𝑥 to solve for 𝐴𝐵.
Do you agree with either of them? Who is correct?

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The two acute angles of a right triangle add up to 90o.
The ratio given for this triangle is sin 𝜃 = 7/25 .
What is the cosine of the other angle?

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If 𝜃 is the number of degrees of one acute angle in a right triangle and sin(𝜃) = 3/5.
Find cos (90 − 𝜃).

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In a 5-12-13 right triangle, 𝜃 is the number of degrees of the smallest angle.
Find sin 𝜃.

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Which one is the easy way to remember trigonometric ratios?

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From ∠C, what side is AB?

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If you are given the two sides that are not the hypotenuse, which trig function should you use?

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If you are given the opposite side and hypotenuse, which trig function should you use?

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If you are given the hypotenuse and an adjacent side, which trig function should you use?

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cos A = _______ 

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tan A = _______ 

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sin X = _______ 

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cos A = _______ 

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If you are given 2 of the sides to an obtuse triangle, which trig function should you use to find the other side?

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Choose the correct ratio.

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Choose the correct ratio.

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Choose the correct ratio.

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Select all the true equations:

Write 1 equation using sine and 1 equation using cosine based on triangle 𝐴𝐵𝐶.

Draw a diagram that will help you explain why sin(𝜃) = cos (90 − 𝜃).

Explain why sin(𝜃) = cos (90 − 𝜃).

Use your knowledge of the relationship between trigonometric ratios to answer each of the following questions. Select all the true equations.

Write 2 expressions that can be used to find the value of 𝑥.

Who is correct?Andre and Mai are discussing how to solve for side 𝐴𝐵. Andre thinks he can use the equation tan(12) = 𝑥/6 to solve for 𝐴𝐵. Mai thinks she can use the equation tan(78) = 6/𝑥 to solve for 𝐴𝐵. Do you agree with either of them? Who is correct?

The two acute angles of a right triangle add up to 90o. The ratio given for this triangle is sin 𝜃 = 7/25 . What is the cosine of the other angle?

If 𝜃 is the number of degrees of one acute angle in a right triangle and sin(𝜃) = 3/5. Find cos (90 − 𝜃).

In a 5-12-13 right triangle, 𝜃 is the number of degrees of the smallest angle.Find sin 𝜃.

Which one is the easy way to remember trigonometric ratios?

From ∠C, what side is AB?

If you are given the two sides that are not the hypotenuse, which trig function should you use?

If you are given the opposite side and hypotenuse, which trig function should you use?

If you are given the hypotenuse and an adjacent side, which trig function should you use?

If you are given 2 of the sides to an obtuse triangle, which trig function should you use to find the other side?

Choose the correct ratio.

Choose the correct ratio.

Choose the correct ratio.

Choose the correct ratio.What is the cosine of angle P?cos P =

Use your knowledge of the relationship between trigonometric ratios to answer each of the following questions.
Select all the true equations.

Who is correct?
Andre and Mai are discussing how to solve for side 𝐴𝐵. Andre thinks he can use the equation tan(12) = 𝑥/6 to solve for 𝐴𝐵. Mai thinks she can use the equation tan(78) = 6/𝑥 to solve for 𝐴𝐵.
Do you agree with either of them? Who is correct?

The two acute angles of a right triangle add up to 90o.
The ratio given for this triangle is sin 𝜃 = 7/25 .
What is the cosine of the other angle?

If 𝜃 is the number of degrees of one acute angle in a right triangle and sin(𝜃) = 3/5.
Find cos (90 − 𝜃).

In a 5-12-13 right triangle, 𝜃 is the number of degrees of the smallest angle.
Find sin 𝜃.

Choose the correct ratio.
What is the cosine of angle P?
cos P =