Sadie’s Concert Question stage_lights by flickr user doctor paradox Microphone by flickr user Gratzer

THE QUESTION: Sadie's stage manager specified that the space they would take up would be equivalent to the sector tan (α + β). α and β aren't directly given but sin α = 12/15, cos β = 12/13 , given that cos α > 0 and sin β > 0.

THE QUESTION:

Sadie's stage manager specified that the space they would take up would be equivalent to the sector tan (α + β). α and β aren't directly given but sin α = 12/15, cos β = 12/13 , given that cos α > 0 and sin β > 0.

On the other hand, the pub owner says that the maximum area he could give the band was 100 m 2 . Using the information above, find the area Sadie's band would require if the radius of the room was 2 metres.

On the other hand, the pub owner says that the maximum area he could give the band was 100 m 2 . Using the information above, find the area Sadie's band would require if the radius of the room was 2 metres.

STEPS PROCESS **There are two ways to find tan (α +β), one way is: Remember that complete information is needed to use the double angle identities. In order to do that, sin β and cos α of the sectors must be found. This is done by drawing a Cartesian plane and drawing triangular sections in the quadrants given. One triangle represents α and the other is β. The lengths of the triangle are found within the given info, ex. sin α = 12/15. cos α is found by using the Pythagorean theorem since they are both right angle triangles. Once the cosine and sine of each type are found, plug it into the formula and the result will be tan (α +β).

STEPS

PROCESS

**There are two ways to find tan (α +β), one way is:

Remember that complete information is needed to use the double angle identities. In order to do that, sin β and cos α of the sectors must be found. This is done by drawing a Cartesian plane and drawing triangular sections in the quadrants given. One triangle represents α and the other is β.

The lengths of the triangle are found within the given info, ex. sin α = 12/15. cos α is found by using the Pythagorean theorem since they are both right angle triangles.

Once the cosine and sine of each type are found, plug it into the formula and the result will be tan (α +β).

STEPS PROCESS The second way to find tan (α +β) is: Draw a Cartesian plane and the triangular sectors in the quadrants given. For triangle. Find the tangent of triangles α and β by using the given info and the Pythagorean theorem. tan = sine cosine Plug in these tangent values into general formula.

STEPS

PROCESS

The second way to find tan (α +β) is:

Draw a Cartesian plane and the triangular sectors in the quadrants given. For triangle.

Find the tangent of triangles α and β by using the given info and the Pythagorean theorem. tan = sine cosine

Plug in these tangent values into general formula.

STEPS PROCESS (4) WAIT! The question is not complete. The area of the space Sadie will take up is needed to determine whether or not they could perform there. This could be found quickly by the means of a ratio. It is known that a circle is 2 π and Sadie takes up this many radians. This is equal to the area out of π r 2 (5) Because that statement is true, plug in the information and isolate the area to find it. (6) Finally, to determine whether or not Sadie and the Po Boys can play at the Round Pub, compare the area needed to the 100 m 2 . Which is less than 100 m 2

STEPS

PROCESS

(4) WAIT! The question is not complete. The area of the space Sadie will take up is needed to determine whether or not they could perform there. This could be found quickly by the means of a ratio. It is known that a circle is 2 π and Sadie takes up this many radians. This is equal to the area out of π r 2

(5) Because that statement is true, plug in the information and isolate the area to find it.

(6) Finally, to determine whether or not Sadie and the Po Boys can play at the Round Pub, compare the area needed to the 100 m 2 .

Sadie and the Po Boys sure rocked the pub so much that it promoted more customers. Across the Universe by flickr user TW Collins

Sadie and the Po Boys sure rocked the pub so much that it promoted more customers.