Find the exact value of sin 165º.
2 answers:
Answer:
(
-
)
Step-by-step explanation:
Using the sine addition formula
sin(a + b) = sinacosb + cosasinb
and the exact values
sin45° = cos45° = , sin60° =
, cos60° =
Given
sin165°
Note that 165° = (120 + 45)°, thus
= sin(120 + 45)°
= sin120°cos45° + cos120°sin45°
= sin60°cos45° - cos60°sin45°
= ( ×
) - (
×
)
= -
= (
-
)
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In both cases there are more than one possible function sutisfying given data.
1. If
- x‑intercepts are (–5, 0), (2, 0), and (6, 0);
- the domain is –5 ≤ x ≤ 7;
- the range is –4 ≤ y ≤ 10,
then (see attached diagram for details) you can build infinetely many functions. From the diagram you can see two graphs: first - blue graph, second - red graph. Translating their maximum and minimum left and right you can obtain another function that satisfies the conditions above.
2. If
- x‑intercepts are (–4, 0) and (2, 0);
- the domain is all real numbers;
- the range is y ≥ –8,
then you can also build infinetely many functions. From the diagram you can see two graphs: first - blue graph, second - red graph. Translating their minimum left and right you can obtain another function that satisfies the conditions above.
Note, that these examples are not unique, you can draw a lot of different graphs of the functions.
Answer: yes, there are more than one possible function
