Answer each question and explain your reasoning.How long is 75% of 60 minutes?
2 answers:
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Answer:
Step-by-step explanation
The given point tells us that the terminal side of
is in the fourth quadrant.
From the diagram in the attachment,
We can use the Pythagoras Theorem to find the length of the hypotenuse of the right triangle.
Let the hypotenuse be . Then,
Now we use the sine ratio;
.
But since the terminal side of is in the fourth quadrant, the sine ratio must be negative.
This implies that;
.
We rationalize the denominator to get;
.
Answer:
a)
b)
c)
d)
Step-by-step explanation:
a) The problem tells us that angle is in the second quadrant. We know that in that quadrant the cosine is negative.
We can use the Pythagorean identity:
Where we have used that the secant of an angle is the reciprocal of the cos of the angle.
Since we know that the cosine must be negative because the angle is in the second quadrant, then we take the negative answer:
b) This angle is in the first quadrant (where the sine function is positive. They give us the value of the cosine of the angle, so we can use the Pythagorean identity to find the value of the sine of that angle:
where we took the positive value, since we know that the angle is in the first quadrant.
c) We can now find by using the identity:
Notice that we need to find , which we do via the Pythagorean identity and knowing the value of the cosine found in part a) above:
Then:
d)
Since
then