Answers:
- sin(G) = 3/5
- cos(G) = 4/5
- tan(G) = 3/4
- csc(G) = 5/3
- sec(G) = 5/4
- cot(G) = 4/3
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Explanation:
For a right triangle, the sine of a reference angle is equal to the opposite over hypotenuse.
sin(angle) = opposite/hypotenuse
cosine involves adjacent over hypotenuse
cos(angle) = adjacent/hypotenuse
tangent involves opposite over adjacent
tan(angle) = opposite/hypotenuse
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In short, we have this list so far
- sin(angle) = opposite/hypotenuse
- cos(angle) = adjacent/hypotenuse
- tan(angle) = opposite/hypotenuse
The other three trig functions are reciprocals of these first three. Cosecant is the reciprocal of sine, secant is the reciprocal of cosine, and cotangent is the reciprocal of tangent.
Meaning, the other three trig ratios are
- csc(angle) = hypotenuse/opposite
- sec(angle) = hypotenuse/adjacent
- cot(angle) = adjacent/opposite
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So,
- sin(G) = opposite/hypotenuse = FH/FG = 24/40 = 3/5
- cos(G) = adjacent/hypotenuse = GH/FG = 32/40 = 4/5
- tan(G) = opposite/adjacent = FH/GH = 24/32 = 3/4
and
- csc(G) = hypotenuse/opposite = FG/FH = 40/24 = 5/3
- sec(G) = hypotenuse/adjacent = FG/GH = 40/32 = 5/4
- cot(G) = adjacent/opposite = GH/FH = 32/24 = 4/3
Answer:
1. (7,-9)
2. (4,0) and (10,0)
3. (3,0) and (-3,0)
4. (0,-9)
5. (-1,-32)
Step-by-step explanation:
To find the vertex use the formula
First make the equation into a quadratic equation.
Now it is in the form
Now we can substitute the values
Now we have 7 as our x value for the vertex we can substitute for y,
So the vertex for 1 is (7,-9)
To find the intercepts for 2 & 3, they basically already give it to you. You just need to find a value for x for x-4 that will equal it to 0 and another for x for x-10 that will equal it to 0.
4 is slightly different but start the same,
Here, c (9) just shows the graph move down 9, so the y intercept = 9.
5 is the same process as 1,
Vertex,
Substitute,
So the vertex is (-1,-32)
The answers would be a and then ctell me if you need an explaination
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