IXL - Sine and cosine of complementary angles (Geometry practice)

Which is equal to

cos

sin

cos

sin

ref_doc_title.

Learn with an example

question

Which is equal to

sin

cos

sin

key idea

The sine (sin) of an acute angle in a right triangle is the ratio of the length of the leg opposite the angle to the length of the hypotenuse.

The cosine (cos) of an acute angle in a right triangle is the ratio of the length of the leg adjacent to the angle to the length of the hypotenuse.

sin

(

)

opposite

hypotenuse

cos

(

)

adjacent

hypotenuse

solution

One way to find an expression that is equivalent to

sin

is to draw a right triangle that has one

angle.

The acute angles in a right triangle are complementary, so the other acute angle has a measure of

–

Using the triangle, you can see that

sin

You can also see that

cos

So,

sin

cos

In general, if

∠

and

∠

are complementary, then

sin

(

)

cos

(

)

and

cos

(

)

sin

(

)

You can use this fact to answer the question, too. You started with

sin

and you know that

–

So,

sin

cos

Looking for more? Try these:

Lesson: Trigonometric ratios

Lesson: Complementary angles

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Teacher tools

Work it out

Not feeling ready yet? These can help:

Q.2Trigonometric ratios with radicals: sin, cos, and tan

Lesson: Trigonometric ratios

Lesson: Complementary angles

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