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Eva8 [605]
3 years ago
5

SinA=(7/25), determine CosA and TanA exactly

Mathematics
1 answer:
bixtya [17]3 years ago
5 0

Answer:

Cos A = 24/25   &  Tan A = 7/24

Step-by-step explanation:

See the attached figure.

Construct a right triangle and sign one angle as A

So, Sin A = opposite/hypotenuse = 7/25

∴hypotenuse = 25 and opposite = 7

∴ adjacent = √(25² - 7² ) = √576 = 24

∴ Cos A = adjacent/hypotenuse = 24/25

And

Tan A = opposite/adjacent = 7/24

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Step-by-step explanation:

We have the sequence:

35, 45, 55, 65.

Notice that each subsequent term is 10 more than the previous term.

Therefore, our common difference is (+)10.

Recursive Rule:

The standard format for the recursive rule is:

f(n)=a, f(n)=f(n-1)+d

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And as determined, our common difference d is 10.

Substitute. Hence, our recursive rule is:

f(1)=35, f(n)=f(n-1)+10

Explicit Rule:

The standard format for the explicit rule is:

f(n)=a+d(n-1)

Where a is the initial term and d is the common difference. So, let’s substitute 35 for a and 10 for d. Hence, our explicit formula is:

f(n)=35+10(n-1)

Now, let’s find the 20th term. We will utilize the explicit rule since the recursive rule can get tedious. Substitute 20 for n because we would like to 20th term. Thus:

f(20)=35+10(20-1)

Evaluate:

\begin{aligned} f(20)&=35+10(19) \\ f(20)&=35+190 \\ f(20)&=225 \end{aligned}

Hence, the 20th term is 225.

5 0
2 years ago
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