Question

What is the relationship between the sine and cosine of the complementary angles in this diagram? drag and drop the answers into the boxes to correctly complete the statements. put responses in the correct input to answer the question. select a response, navigate to the desired input and insert the response. responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. responses can also be moved by dragging with a mouse. both cos(17°) and sin(x°) can be represented by the ratio response area. the angles measuring 17° and x° are complementary angles. this means x° 17° = response area. therefore, x = response area. since cos(17°)=sin(x°), this also shows that cos(17°)=sin(response area)°.

Answer 1

The sine and cosine of complementary angles can be related using the equation sin(x) = cos(90 - x) or cos(17) = sin(x).

Step-by-step explanation:

The relationship between the sine and cosine of complementary angles is as follows:

• If the sine of one angle is equal to the cosine of another angle, then their sum equals 90 degrees; that is, sin(x) = cos(90 - x).
• Therefore, if we have two complementary angles, one measuring 17 degrees and the other measuring x degrees, we can write the equation sin(x) = cos(17).
• Using this equation, we can determine the value of x by taking the inverse sine of both sides: x = arcsin(cos(17)).
• Since cos(17) is equal to sin(x), we can further simplify the equation to cos(17) = sin(x) degrees.