{"id":9326,"date":"2023-05-04T10:00:57","date_gmt":"2023-05-04T04:30:57","guid":{"rendered":"https:\/\/www.aplustopper.com\/?p=9326"},"modified":"2023-05-05T09:12:48","modified_gmt":"2023-05-05T03:42:48","slug":"trigonometry-solving-angle","status":"publish","type":"post","link":"https:\/\/www.aplustopper.com\/trigonometry-solving-angle\/","title":{"rendered":"Trigonometry: Solving for an Angle"},"content":{"rendered":"
The initial set up for solving these problems will be the same as that for finding a missing side.<\/p>\n
To finish the problem, however, it will be necessary to use a calculator function referred to as an “inverse function” to find the actual number of degrees in the angle.<\/p>\n
The inverse functions, on the graphing calculator, for each of the three trigonometric functions are found directly above the buttons for sine, cosine and tangent. They appear as sin-1<\/sup><\/strong>, cos-1<\/sup><\/strong> and tan-1<\/sup><\/strong>. You will discover, in later courses, that there are actually many angles whose sine is x, but in this course, we are looking for the simplest, most basic angle that has a sine x.<\/p>\n You can think of the inverse functions as “undoing” the trigonometric functions, leaving us with just the angle. Set Up the Diagram:<\/strong> Set Up the Formula: <\/p>\n","protected":false},"excerpt":{"rendered":" Trigonometry: Solving for an Angle Using Trigonometric Functions to Find a Missing Angle The initial set up for solving these problems will be the same as that for finding a missing side. To finish the problem, however, it will be necessary to use a calculator function referred to as an “inverse function” to find the […]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[5],"tags":[3431,146,3430],"yoast_head":"\n
\nNote: sin-1<\/sup>(x) is read “the angle whose sine is x”.<\/p>\n
\nsin-1<\/sup>(sin x) = x<\/strong>
\nAs your study of trigonometric inverse functions continues, you will see that sin-1<\/sup>(x)<\/strong>, cos-1<\/sup>(x)<\/strong> and tan-1<\/sup>(x)<\/strong> may also be written as arcsin(x)<\/strong>, arccos(x)<\/strong>, and arctan(x)<\/strong>, which are read “the arc whose sine is x”, and so on.<\/p>\n
\nFind x, to the nearest degree.
\n
\nNotice that in this problem, the x is INSIDE the triangle representing the angle. The a is alone, so this problem deals with o and h, which is sine.<\/p>\n
\n<\/strong>
\nNow, divide 30 by 40 to change the fraction to a decimal.
\nsin x = 0.75
\nThe goal now is to find an angle whose sine is 0.75. To do this, use the sin-1<\/sup> function on your calculator!
\nOn the graphing calculator: activate sin-1<\/sup> (above the sin key) and then enter 0.75.
\nOn the scientific calculator: enter 0.75 and then activate the sin-1<\/sup> above the sin key.
\nBe sure you are in DEGREE MODE.
\n<\/p>\n