You already know what the sine, cosine and tangent of an angle are. The problem is that, apart from a few special angles ($30^\circ$, $45^\circ$, $60^\circ$...), their exact value cannot be worked out by hand: you need a calculator, and you have to know how to use it accurately, because one wrong button press gives a result that looks correct but is completely wrong.
Calculate, using your calculator and rounding to four decimal places, the value of the following direct trigonometric ratios: $\sin 34^\circ$, $\cos 78^\circ$, and…
Calculate, using your calculator and rounding to four decimal places, the value of the following direct trigonometric ratios: $\sin 34^\circ$, $\cos 78^\circ$, and $\tan 12^\circ$.
An angle does not always come in whole degrees: $37^\circ 42' 15''$ means $37$ degrees, $42$ minutes ($1^\circ = 60'$) and $15$ seconds ($1' = 60''$). The calculator has a key (usually $\boxed{^\circ \, ' \, ''}$) for entering and converting these values.
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Find the value of the following trigonometric ratios, expressing the result to three decimal places. Make sure you correctly enter degrees, minutes, and seconds into…
Find the value of the following trigonometric ratios, expressing the result to three decimal places. Make sure you correctly enter degrees, minutes, and seconds into your calculator: $\sin(45^\circ 12' 30'')$, $\cos(12^\circ 5')$, and $\tan(89^\circ 0' 10'')$.
A surveyor measures an angle of inclination on a slope of $14^\circ 25'$. Calculate the tangent of this angle to four decimal places to find the gradient coefficient of…
A surveyor measures an angle of inclination on a slope of $14^\circ 25'$. Calculate the tangent of this angle to four decimal places to find the gradient coefficient of the land.
Inverse functions: from the value of the ratio to the angle
If you know the value of $\sin \alpha$ and want to find $\alpha$, you use the inverse function: $\sin^{-1}$ (or $\arcsin$), normally with the $\boxed{\text{SHIFT}}$ or $\boxed{\text{2ndF}}$ key followed by $\boxed{\sin}$.
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Use the inverse calculator function to find the acute angle $\alpha$, expressed in degrees, minutes, and seconds, given that $\sin \alpha = 0,456$.
Use the inverse calculator function to find the acute angle $\alpha$, expressed in degrees, minutes, and seconds, given that $\sin \alpha = 0,456$.
On a warehouse loading ramp, the total length of the ramp is $15 \text{ m}$ and the vertical height it covers is $2,5 \text{ m}$. Calculate the angle of inclination of…
On a warehouse loading ramp, the total length of the ramp is $15 \text{ m}$ and the vertical height it covers is $2,5 \text{ m}$. Calculate the angle of inclination of the ramp with respect to the horizontal, expressing it in degrees and minutes.
Most scientific calculators do not have a direct key for $\sec$, $\csc$ or $\cot$: you have to calculate $\cos$, $\sin$ or $\tan$ first, and then take the reciprocal with the $\boxed{x^{-1}}$ or $\boxed{1/x}$ key.
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Calculate, rounding to three decimal places, the value of the reciprocal trigonometric ratios $\sec 55^\circ$, $\csc 20^\circ$, and $\cot 70^\circ$. Remember to use the…
Calculate, rounding to three decimal places, the value of the reciprocal trigonometric ratios $\sec 55^\circ$, $\csc 20^\circ$, and $\cot 70^\circ$. Remember to use the fundamental reciprocal identities on your calculator.
Given that $\sec \alpha = 1,8$ and that $\alpha$ is an acute angle, use the calculator to find first the value of $\alpha$ in degrees, minutes, and seconds, and then…
Given that $\sec \alpha = 1,8$ and that $\alpha$ is an acute angle, use the calculator to find first the value of $\alpha$ in degrees, minutes, and seconds, and then calculate the value of $\sin \alpha$ rounded to three decimal places.
An angle can also be measured in radians: one complete turn is $360^\circ$ or $2\pi$ radians. The calculator has a mode for each unit (DEG / RAD), and you have to select it with the MODE key (or SHIFT + MODE, SETUP, depending on the model) and check the DEG/RAD indicator on the screen before calculating, not by guesswork.
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Express in radians the following angles given in degrees, using the value of $\pi$ on your calculator and rounding to three decimal places: $40^\circ$, $115^\circ$, and…
Express in radians the following angles given in degrees, using the value of $\pi$ on your calculator and rounding to three decimal places: $40^\circ$, $115^\circ$, and $250^\circ$.
Calculate the value of $\sin(1,2)$ and $\cos(0,8)$ assuming that the angles are in radians. Express the result to four decimal places after correctly setting your…
Calculate the value of $\sin(1,2)$ and $\cos(0,8)$ assuming that the angles are in radians. Express the result to four decimal places after correctly setting your calculator mode.
Evaluate the following trigonometric expression assuming that the angles are given in radians: $M = \sin(1,5) \cdot \cos(0,5) - \tan(0,8)$. Express the final result…
Evaluate the following trigonometric expression assuming that the angles are given in radians:
$M = \sin(1,5) \cdot \cos(0,5) - \tan(0,8)$.
Express the final result rounded to three decimal places.