During a trigonometry lesson a group of students made some predictions about what they expected to find for the values of the trigonometric functions of some angles. They then found the sine, cosine and tangent of 25° and 50°. (i) In the table given, show, correct to three decimal places, the values they found. sin 25° = cos 25° = tan 25° = sin 50° = cos 50° = tan 50° = (ii) Maria said: "The value from any of these trigonometric functions will always be less than 1." Was Maria correct? Give a reason for your answer. Answer: Reason: (iii) Sharon said: "If the size of the angle is doubled then the value from any of these trigonometric functions will also double." Was Sharon correct? Give a reason for your answer. Answer: Reason: (iv) James said: "The value from all of these trigonometric functions will increase if the size of the angle is increased." Was James correct? Give a reason for your answer.

Junior Cycle Mathematics Trigonometry: During a trigonometry lesson a g

During a trigonometry lesson a group of students made some predictions about what they expected to find for the values of the trigonometric functions of some angles - Junior Cycle Mathematics - Question 12 - 2014

Question 12

During a trigonometry lesson a group of students made some predictions about what they expected to find for the values of the trigonometric functions of some angles.... show full transcript

Worked Solution & Example Answer:During a trigonometry lesson a group of students made some predictions about what they expected to find for the values of the trigonometric functions of some angles - Junior Cycle Mathematics - Question 12 - 2014

Step 1

sin 25° =

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Using a calculator, we find that the value of $ext{sin}(25°)$ is approximately $0.423$ .

Step 2

cos 25° =

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Calculating the cosine of $25°$ , we get $ext{cos}(25°) hickapprox 0.906$ .

Step 3

tan 25° =

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The tangent of $25°$ is calculated as $ext{tan}(25°) hickapprox 0.466$ .

Step 4

sin 50° =

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For the sine of $50°$ , the result is $ext{sin}(50°) hickapprox 0.766$ .

Step 5

cos 50° =

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The cosine of $50°$ is approximately $ext{cos}(50°) hickapprox 0.643$ .

Step 6

tan 50° =

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Finally, the value of the tangent is $ext{tan}(50°) hickapprox 1.192$ .

Step 7

Was Maria correct? Give a reason for your answer.

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Maria was not correct. For example, the value of $ext{tan}(50°)$ is greater than $1$ .

Step 8

Was Sharon correct? Give a reason for your answer.

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Sharon was not correct. None of the values above doubled when the angle was doubled from $25°$ to $50°$ .

Step 9

Was James correct? Give a reason for your answer.

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James was not correct. For example, the value of $ext{cos}(50°)$ actually decreased when the angle was increased from $25°$ to $50°$ .

During a trigonometry lesson a group of students made some predictions about what they expected to find for the values of the trigonometric functions of some angles - Junior Cycle Mathematics - Question 12 - 2014

Worked Solution & Example Answer:During a trigonometry lesson a group of students made some predictions about what they expected to find for the values of the trigonometric functions of some angles - Junior Cycle Mathematics - Question 12 - 2014

sin 25° =

cos 25° =

tan 25° =

sin 50° =

cos 50° =

tan 50° =

Was Maria correct? Give a reason for your answer.

Was Sharon correct? Give a reason for your answer.

Was James correct? Give a reason for your answer.

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