I am taking an online class, and cant understand why when I calculate ona ti84 plus an answer I get decimal answer and my teachers answer is sq root, is there something I am not doing on my calculator? How do I convert.
Example, teachers answer to the following was
sin 315deg = -sin 45deg = -sqrt2/2
I got a decimal answer.
You should become familiar with two important special triangles
1. the 45-45-90 right-angled triangle whose sides are in the ratio
1 : 1 : √2
2. the 30-60-90 right-angled triangle whose sides are in the ratio of
1 : √3 : 2
The question to find sin 315° probably says to find it "exactly"
I do these in a 3-step process
1. Where is the angle?
315 is in IV and in IV the sine is negative
2. How far from the x-axis ?
315° is 45° from the x-axis
The answer to this question will always be an angle between 0 and 90, it will be called the "angle in standard position, or ASP)
3. Rewrite the question in terms of the ASP
sin 315 = -sin 45
From your special triangles
sin 45 = 1/√2 or √2/2 after rationalizing
so sin 315 = -sin 45 = -√2/2
In the matrix below, which element is a1,2?
1
4
7
2
5
8
3
6
9
A. 8 C. 6
B. 5 D. 2
Examination
When you're using a calculator to calculate trigonometric functions like sin, cos, or tan, the default setting on most calculators is to provide results in decimal form. However, it is possible to change the calculator's settings to display results in fractional or radical form, which can be more preferable for some calculations.
To convert a decimal answer into a radical or fractional form on a TI-84 Plus calculator, you can use the built-in "math" functions. Here's how you can perform this conversion:
1. Enter the decimal value you obtained from your calculator.
2. Press the "MATH" button on your calculator.
3. Select the "Frac" option by pressing the corresponding number/button, usually 1.
4. If the result is a repeating decimal, the calculator will display it as a fraction.
5. If the result is an irrational number or cannot be expressed exactly as a fraction, the calculator will approximate it using radicals or fractions.
In your example, when calculating sin 315°, the decimal value you obtained can be converted to a radical or fractional form. Follow the steps above to convert it on your calculator.
However, it's important to note that the reason your teacher's answer involves square roots is due to trigonometric identities or properties. In this case, sin 315° can be simplified using the sum-to-product identity for trigonometric functions:
sin(A - B) = sin A · cos B - cos A · sin B
In this case, sin 315° can be expressed as the negative of sin 45°. Since sin 45° is equal to √2/2, the answer becomes -√2/2.
So, if you want to achieve the same answer as your teacher, you can either manually apply the trigonometric identity or use the calculator's conversion feature to display the result in radical or fractional form.