Which of the following are exterior angles? Check all that apply
2 answers:
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Answer: C. - √2
Step-by-step explanation:
<u>Given requirements from the question</u>
Find the exact value of sec 135°
<u>Convert into common trigonometric expression</u>
sec = secant
secx = 1 / cosx
Therefore, sec 135° = 1 / (cos 135°)
<u>Find the reference angle</u>
135° is quite a complicated angle, but it is possible to simplify it by finding its reference angle.
Since 135° is in the second quadrant, its reference angle will be
180° - 135° = 45°
However, we need to consider the positive and negative.
In a coordinate plane, the clue is (A S T C), which corresponds to the positive values in each quadrant. In the QI, "All" are positive. In the QII, sine is positive. In the QIII, the tangent is positive. In QIV, cosine is positive.
Therefore, when the value of cosine is in QII, it is negative.
The reference angle = - (1 / cos 45°)
<u>Determine the final value</u>
Given that the reference angle = - (1 / cos 45°)
cos 45° = 1 / √2
Therefore:
sec 135° = - (1 / cos 45°) = - (1 / (1 / √2)) =
Hope this helps!! :)
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Answer: (C) 16
Step-by-step explanation:
Given : Number of sizes of self-stick notepads= 2
Number of colors = 4
Type 1 : The store packs the notepads in packages that contain 3 notepads of the same size.
i.e. By Fundamental principle of counting , we have
Number of different packages possible = Number of colors x No. of sizes
=
Type 2: Notepads of the same size and of 3 different colors.
Choices for 3 different colors out of 4 :
Again by fundamental principle :
Number of different packages possible = No. of choices for choosing 3 different colors x No. of sizes
=
From Type 1 and Type 2 , the total number of different packages of the types described above are possible =8+8= 16
Hence, the correct answer is option (c) 16.